Introduction to 2D shapes
expand_moreIntroduction to 2D shapes - Khan Academy
2D shapes are shapes with two dimensions, such as width and height. An example of a 2D shape is a rectangle or a circle. 2D shapes are flat and cannot be physically held, because they have no depth; a 2D shape is completely flat.
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thumb_up thumb_downIntroduction to 2D shapes
- Dimensions are referred to as measures of size such as length, width, base and height of an object or a shape.
- Length - Length refers to the longest dimension of an object, measured horizontally or left to right.
- Base - Refers to both the side and its length (the measurement). Height is usually perpendicular to the base.
- Height - The measurement of someone or something base to top, measure vertically or down-up.
- Width - the measurement or extent of something from side to side.
- 2D shapes are therefore consists of two of these dimensions.
Perimeter
expand_morePerimeter - Math Antics
A 1 dimensional quantity that measures the total length around the outside of a shape.
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thumb_up thumb_downWhat is Area?
expand_moreWhat is Area - Math Antics
A 2 dimensional quantity, measuring the amount of space inside a 2D shape.
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thumb_up thumb_downArea
- A 2 dimensional quantity, measuring the amount of space inside a 2D shape.
- Measured in unit squared, e.g., cm2, m2, etc.
- A = Length x Width
- Length being the longer side and Width the shorter side.
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- Calculate the area of a rectangle with a length of 10 cm and With of 6 cm
- A = L x W
- A = 10 cm x 6 cm
- A = 60 cm2
- Since unlike a rectangle, all side of a square are equal.
- Hence, we can not distiguish the sides in terms of Length and Width,
- The area of a square is usually calculated using A = side x side or A = side2.
- Calculate the area of a square with sides of 10 cm.
- A = s2
- A = 10 cm2
- A = 100 cm2
- When you cut a rectangle exactly in half along a diagonal line from opposite corners, you get two right-angle triangles with each exactly half of the cut rectangle.
- Each right-angle triangle therefore has half the area of the rectangle.
- Therefore, area of a right-angle triangle = (L * W)/2.
- However, the names Length and Width, will not work well for acute and obtuse because it would be hard to tell which one is length and width.
- Instead, we choose one of the three sides to be base and the one perpendicular to the base, is height.
- Hence, formula for Traingles Area is A = (B * H)/2
- Calculate the area of a right-angle triangle with sides of 10 cm.
- A = (B * H)/2
- A = (9m * 4m)/2
- A = 18m2
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- A = ((sum of the parallel lines) * height)/2
- Calculate the area of a trapezium with opposite sides equal to 10 cm and 15 cm respectively, with a height of 11 cm.
- A = ((sum of the parallel lines) * height)/2
- A = ((a + b) * h)/2
- A = ((10 + 15) * 11cm)/2
- A = 137.50 cm2
Area of a rectangle
Area of a square
Area of a triangle
Area of a Trapezium
Given a square below with a side = 0 cm
Calculate the perimeter of the square.
Chances: 2
You get two chances for this question.
Calculate the area of the square.
✔️❌Chances: 2
You get two chances for this question.
given the triangle below, with a = 0mm, b = 0mm, and c = 0mm. Find the area of the triangle.
Chances: 2
You get two chances for this question.
Find the area of the football field below, if its width = 0m and length = 0m.
Chances: 2
You get two chances per question.
- The first question you got 0/2
- The second question you got 0/2
- The third question you got 0/2
- The fourth question you got 0/2
Your total is therefore, 0/8.
Percentage
%
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Introduction to Circles
expand_moreCircles - Math Antics
A 1 dimensional quantity that measures the total length around the outside of a shape.
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thumb_up thumb_downCircles
- Circles are 2d shape formed when a set of points equidistant from a fixed point is called a circle.
- We already know that the distance around a 2d shape is called a perimeter. However, in circles, this is referred to as circumference.
- The distance between any point of the circumference and the center is called the radius.
- The distance between any two points of the circumference through the center is called the diameter.
- The diameter is two times the radius.
- Therefore, diameter = 2* radius and radius = diameter/2.
- Pi = is the ratio of the circumference and diameter of any given circle, and it is always the same.
- Therefore,
- Pi or π = circumference/diameter
- The value of pi is irrational, so it is usually represented as a two-decimal places number of 3.14.
Area of a Circle
expand_moreArea of a circle - Math Antics
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thumb_up thumb_downArea of the circle
- A = π * r2
- r is the radius
Circumference equation
- C = π * d
- d is the diameter of the circle
- or
- C = π * 2r
- Please do not confuse r2 with 2r
- r2 = r * r
- Whereas, 2r = r + r
Find the area of the circle if radius is equal to 10 m
- A = π * r2
- A = 3.14 * 10m2
- A = 314m2
Find the circumference of the circle
- C = π * 2r
- C = 3.14 * 2 * 10m
- C = 6.28 * 10m
- C = 62.8m
The circular fish pond below has a radius of 0m, find its area.
Your answer into 2 decimal places.
Chances: 2
You get a maximum of two chances for this question.
Given the circle with an area of 0m2, find the diameter of the circle.
Chances: 3
You get a maximum of three chances for this question.
Now, find the circumference of that circle.
✔️❌Chances: 2
You get a maximum of two chances for this question.
- The first question you got 0/2
- The second question you got 0/3
- The third question you got 0/2
Your total is therefore, 0/7.
Percentage
%
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Introduction to 3D shapes
expand_moreIntroduction to 3D shapes - Cognito
3D shapes, or three-dimensional shapes, have three dimensions: length, width, and height. They occupy space and have volume, distinguishing them from 2D shapes, which only have length and width.
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thumb_up thumb_down3D shapes
- 3D shapes, or three-dimensional shapes, have three dimensions: length, width, and height. They occupy space and have volume, distinguishing them from 2D shapes, which only have length and width.
- Here are some common 3D shapes:
- Cube: All faces are squares, and all edges are equal.
- Cuboid (Rectangular Prism): Faces are rectangles, and opposite faces are equal.
- Pyramid: A base that is a polygon (commonly a square or triangle) with triangular faces converging to a single point (vertex).
- Tetrahedron: A pyramid with a triangular base and four triangular faces.
- Cylinder: Has two parallel circular bases connected by a curved surface.
- Cone: Has a circular base and a single vertex, with a curved surface connecting them.
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- Sphere: Every point on the surface is equidistant from the center.
- Hemisphere: A three-dimensional shape that's half of a sphere with one flat, circular side..
Calculating the surface area
expand_moreCalculating the surface area - Professor dave
The area occupied by a three-dimensional object by its outer surface.
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thumb_up thumb_downSurface Area
The sum of all areas of faces of a polyhedral.
Faces are all the two-dimensional shapes that are found in a 3d shape.
-
Cube
A cube is made of 6 square face; therefore, the surface area of a cube is a2+ a2 + a2 + a2 + a2 + a2.
Factor our a2:
a2(1+1+1+1+1+1+1)
Therefore, the final equation is a2(6). -
Cuboid or rectangular prism
A rectangle prism comprises of 3 different rectangles based on length, Width, or Height, with each rectangle going in pairs.
The first pair comprises the 2 dimensions of height & length (LH), in the diagram above these, are front and back triangles.
The second pair is made up of the 2 dimensions of length and width (LW), in the diagram above the top and bottom triangles.
The third pair is one made up of 2-dimension of height and width (HW), in the diagram above these are right and left triangles.
Is the sum of all the 3 different triangles multiplied by two, because they all go in pairs.
SA = 2*LH + 2*LW + 2*HW
Factor out 2:
The final equation is then:
SA = 2(LH + LW + HW) -
Square pyramid
Made up 1 square and 4 triangles.
Therefore, the surface area of the square prism is the sum of the areas of all its triangles plus the area of that one square.
Area of a square = s2
Area of a triangle = (b *h)/2 or ½(b * h)
SA = s2 + (b *h)/2 + (b *h)/2 + (b *h)/2 + (b *h)/2
SA = s2 + 4(b *h)/2
SA = s2 + 2(b*h)
h is the slant height of the pyramid. -
Triangle pyramid
The sum of areas of all its 4 triangles.
The base triangle is usually equilateral. Then you can use the following equation to find its area:
A = √4/2 * S2
Surface Area of the Triangle = A + 3/2(b * h)
A - is the area of the base triangle. -
Cylinder
Made up of 2 equal circles and a curved rectangle.
Therefore, the surface area of a cylinder is the sum of the two circles and the curved rectangle.
Area of a circle = πr2
Area of a rectangle = L x W, where Width is equal to the Height of the cylinder and Length is equal to the circumference of the base circle. Circumference of the circle = π2r
Therefore, the cylinder surface area = πr2 + πr2 + π2r
SA = 2 πr2+ hπ2r -
Cone
Made up of 1 circle and a curved triangle.
Area of a circle + πrl
L is the slant height of the cone.
Therefore, the surface area of a cone = πr2 + πrl
-
Sphere
Every point on the surface is equidistant from the center.
Therefore,
Surface Area of a sphere = 4πr2
A cylindrical water tank with a height of 0mm, with a diameter of 0mm.
Find the surface area of the water tank.
Chances: 3
You get a maximum of three chances for this question.
A cone fitting exactly to the top of the tank is added to the tank forming the shape below. The slant height of the cone is 0mm.
Find the total surface area
Chances: 4
You get a maximum of four chances for this question.
Find the area of a sphere with a radius of 0m.
Chances: 2
You get a maximum of two chances for this question.
- The first question you got 0/3
- The second question you got 0/4
- The third question you got 0/2
Your total is therefore, 0/7.
Percentage
%
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Calculating the Volume
expand_moreCalculating the Volume - Professor dave
Volume is a measure of the amount of space occupied by a three-dimensional object.
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thumb_up thumb_downVolume equations for each 3d shape
Cube:
Volume = a3
where a
a is the length of a side.Cuboid:
Volume= L * W * H
Where L is the length
W is the width,
and H is the height.Pyramid:
Volume = 1/3(B * H)
Where
B is the area of the base and
h is the height perpendicular to the base, not the slant height.Cone:
Volume = 1/3(πr2h)
Where
πr2 is the area of the circle of the cone and
h is the height.Cylinder:
Volume= πr2* h
Where
r πr2 is the area of the bottom circle and
h is the height.Sphere:
Volume = 4/3(πr3)
Given LION EXTRA LONG ECO SAFETY MATCH BOx with a length of 0mm , width of 0mm , and height of 0mm.
Calculate its surface area.
Chances: 3
You get a maximum of three chances for this question.
Calculate the volume of the matchbox.
Chances: 3
You get a maximum of three chances for this question.
A cylindrical water bottle with a height = 0cm, and diameter of the base = 0cm.
Calculate the volume of the bottle.
Chances: 3
You get a maximum of three chances for this question.
The water bottle is filled with water to the top. Using the hemispherical lid that fit exactly to the top of the water bottle to drink.
How many full lids will it take to drink all the water inside the bottle?
Chances: 4
⚠️Roundoff into two decimal places.
You get a maximum of four chances for this question.
A square pyramid with a volume of 0cm3, B = 0cm. Find the length of AC.
Chances: 3
You get three chances for this question.
Find the slant height.
Chances: 3
You get a maximum of three chances for this question.
Line AC is exactly at the center of the square base. Determine the total surface area of the pyramid.
Chances: 3
You get a maximum of three chances for this question.
- The First question you got 0/3
- The Second question you got 0/3
- The Third question you got 0/3
- The fourth question you got 0/4
- The Fifth question you got 0/3
- The Sixth question you got 0/3
- The Seventh question you got 0/3
Your total is therefore, 0/0.
Percentage
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The box is now pushed horizontal to the right by a force of 0N is moving to the right with an acceleration of 0m/s2, what is the coefficient of the kinetic friction?
Chances: 3
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The box is now pushed at angle of 0° to the right by a force of 0N, Calculate the new normal force.
Chances: 3
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As the box continue to move, what is the acceleration of the box if kinetic friction coeffient was 0.
Chances: 3
You get a maximum of three chances for this question.