## HVAC Trade Math: Chapter 2

**Geometry**

## In this module, we will talk about different shapes and how to find their area, perimeter, and volume. __Skip to quiz!__

**Overview**

Two-dimensional shapes are formed on a flat surface. 2D shapes have two dimensions: **length **and** width**. They have no depth.

For example, anything we draw or write on a piece of paper is two-dimensional. This is because the paper is entirely flat.

Two-dimensional shapes are all around us. Some examples of 2D shapes include square, rectangle, circle, and triangle.

3D shapes have three dimensions: length, width, and thickness. Examples of 3D shapes include cube, cone, sphere, etc.

3D shapes are everywhere. A dice is an example of a cube.An ice cream cone is an example of cone. A soccer ball is an example of a sphere.

**Area**

Area is the amount of space a shape takes up on a flat surface. 2D shapes have two dimensions: length and width. This is why area is calculated using **squared units** such as cm² and m².

To find the area of any shape, all we need is the length and the width. Let’s take a look at how we can find the area of shapes such as square, rectangle, and triangle.

**Perimeter**

Perimeter is the total length of all the sides of a 2D shape. To calculate the perimeter of any shape, we add up the length of each side. Let us look at how to calculate the perimeter of a square, rectangle, and triangle.

**Volume**

Volume is the space a three-dimensional shape takes up. 3D shapes have three dimensions: length, width, and thickness. Volume is calculated in **cubic units** such as cm³ and m³.

Similar to calculating area and perimeter, different equations are used to calculate the volume of different shapes. Let’s take a look at how we can find the volume of shapes such as cube, cone, and sphere.

**Circles**

A circle is a round shape that has no corners. The distance from the center of a circle to any point on the edge of a circle is the same. This distance is called the radius. The distance from one side of the circle to another is called the diameter.

2D shapes have length and width. A triangle, a square, a rectangle are all 2D shapes. A circle is a 2D shape with no corners.

3D shapes have length, width, and thickness. Cubes, cones, and spheres are examples of 3D shapes.

**Question #1: Two dimensional objects only have length and width. **

True

False

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Answer: **True**

*Two-dimensional objects are flat; therefore, they have no thickness, only length and width. *

**Question #2: 3 dimensional objects have length, width, and thickness. **

True

False

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Answer: **True**

*3D shapes have three dimensions: length, width, and thickness.*

**Question #3: What unit is area calculated in? **

Squared unit

Cubic unit

No unit

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Answer: **Squared unit.**

*Two-dimensional objects are flat; therefore, they have no thickness, only width and length.*

**Question #4: What is the area of a square that has a length and width of 2 inches? **

4 in²

5 in²

6 in²

8 in²

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Answer: **4 in²**

*Use the equation A = s x s to calculate the area of the square. *

A = 2 x 2

= 4

**Question #5: What is the area of a rectangle that has a length of 2 meter and a width of 3m ? **

6 m

5

6 m²

2 m²

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Answer: **6 m²**

*Use the equation A = l x w to calculate the area of the rectangle. *

A = 2 x 3

= 6

**Question #6: What is the area of a triangle that has a height 4 feet and base of 2 feet? **

8 ft²

6 ft²

4 ft²

2 ft²

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Answer: **4 ft²**

*Use the equation A = ½ (b x h) to calculate the area of the triangle. *

A = ½ (4 x 2)

= ½ (8)

= 4

**Question #7: What is the perimeter? **

The space a shape takes up.

The total length of the shape

None of the above.

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Answer: **The total length of the shape**

*Perimeter is the total length of the shape when all the sides are added up. *

**Question #8: Find the perimeter of a square with a length of 2 inches. **

8 in

4 in

6 in

2 in

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Answer: **8 in**

*Use the formula *

*P = 4 x a to calculate the perimeter of a square.*

*P = 4 x 2*

* = 8 *

**Question #9: Find the perimeter of a rectangle with a length of 2 inches and width of 3 inches. **

10 in

6 in

4 in

5 in

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Answer: **10 in**

*Use the formula *

*P = 2 x (w + h) to calculate the perimeter of a rectangle.*

*P = 2 x (2 + 3)*

* = 2 x 5*

* = 10*

**Question #10: Find the perimeter of a triangle that has a length of 3 inches on all three sides. **

9 in

6 in

3 in

4 in

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Answer: **9 in**

*Use the formula *

*P = a + b + c to calculate the perimeter of a triangle. *

*P = 3 + 3 +3 *

* = 9*

**Question #11: What unit is volume calculated in. **

Squared unit

Cubic unit

No unit

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Answer: **Cubic unit**

*Volume is three-dimensional. In 3D, a shape has length, width, and thickness. *

**Question #12: Find the volume of a cube whose sides are 2 inches.**

8 in³

8 in

4 in³

4 in

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Answer: **8 in³**

*Use the equation V = S³ to calculate the volume of a cube. *

*V = 2³*

* = 8 *

**Question #13: Find the volume of a cone that has a radius of 1 and a height of 2. **

2.09 in³

1.09 in

2.0 in³

3.0 in³

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Answer: **2.09 in³**

*Use the equation *

*V = ⅓ ( r² x h) x π. *

*to calculate the volume of a cone. Remember, π = 3.14*

*V = ⅓ (1² X 2) x π*

* = ⅓ (2) x π*

* = ⅔ x π*

* = 2.09*

**Question #14: Find the volume of a sphere with a radius of 3 inches. **

**113.1 in³**1.19 in

1.19 in³

2.78 in³

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Answer: **113.1 in³**

*Use the equation *

*V = 4/3 (π x r³) *

*to calculate the volume of a sphere. Remember π = 3.14.*

*V = 4/3 (π x 3³)*

* = 4/3 (27π)*

* = 113.1 *in³

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