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### Area of triangles

Unit 5

Getting the idea

- Area is a measure of the number of square units needed to cover a region.
- Square Unit is a square with a side length of 1 of any particular unit of measure.
- Square Inches = in2
- Square Centimeters = cm2

1. What is the area of the triangle?

- Step One: Determine the formula for the area of a triangle.
- A = ½ bh
- Step Two:Substitute the values for the baseand the height

into the formula.

- The base, b, measures 8 inches and the height, h, measures

4 inches.

- A = ½ (8)(4)
- Step Three: Multiply
- A = ½ (8)(4)
- A = ½ (32) = ● =
- A = *divide by 2*
- A = 16
- Step Four: Write the answer with correct unit of measure squared.
- Area = 16 in2

4 in

8 in

Right Triangle

- Remember that a right triangle has a hypotenuse and 2 sides called legs.
- The legs form a right angle.
- To find the area of a right triangle, use the legs as the base and height.

Hypotenuse

2. What is the area of the triangle?

- Step One: Determine the formula for the area of a triangle.
- A = ½ bh
- Step Two:Substitute the values for the base and the heightinto the formula.
- The base, b, measures 9 cm and the height, h, measures 3 cm.
- A = ½ (9)(3)
- Step Three: Multiply
- A = ½(9)(3)
- A = ½ (27) = ● =
- A = *divide by 2*
- A = 13.5
- Step Four: Write the answer with correct unit of measure

squared.

- Area = 13.5 cm2

3 cm

9 cm

In an obtuse triangle, you can extend a side to find the height.

Obtuse Angle: Angle greater than 90˚

3. What is the area of the triangle?

- Step One: Determine the formula for the area of a

triangle.

- A = ½ bh
- Step Two:Substitute the values for the base and the height

into the formula.

- The base, b, measures 12 feet and the height, h, measures 5 feet.
- A = ½ (12)(5)
- Step Three: Multiply
- A = ½(12)(5)
- A = ½ (60) = ● =
- A = *divide by 2*
- A = 30
- Step Four: Write the answer with correct unit of measure squared.
- Area = 30 ft2

5 ft

12 ft

4. What is the height of a triangle with an area of 40m2and a base of 10 m?

- Step One:Determine the formula for the area of a triangle.
- A = ½ bh
- Step Two:Substitute the values for the areaand the base into the formula.
- The Area , A, is 40 m2 and the base, b, measures 10 m.
- 40 = ½ (10)(h)
- Step Three: Solve the Equation
- 40 = ½ (10)(h) = ● (h) = (h) = 5h
- 40 = 5h *divide both sides of equal sign by 5 (isolate the variable)
- 8= h
- Step Four: Write the answer with correct unit of measure.
- height = 8 m

5. The Clarke family built a triangular deck at the back of their house. What Is the area of the triangular deck if the base is 9 yards and the height is 7 yards?

- Draw the triangular deck and label the base and the height.
- Write the formula for finding the area of a triangle.
- Substitute the base and height into the formula.
- Solve the formula to determine the area of the triangular deck.

6. A triangular pennant has a base that is 18 inches long and a height of 6 ½ inches. What is the area of the pennant?

- Draw the triangular pennant and label the base and the height.
- Write the formula for finding the area of a triangle.
- Substitute the base and height into the formula.
- Solve the formula to determine the area of the triangular pennant.

7. The Area of a triangle is 30 yd2 and its height is 6 yd. What is the length of the base?

- Write the formula for finding the area of a triangle.
- Substitute the Area and height into the formula.
- Solve the formula to determine the base of the triangle.

8. Mr. Butler drew these two triangles on the board:

34 in

34 in

- 1. What is the area of Triangle A?
- 2. What is the area of Triangle B?
- 3. Describe what you notice about the two triangles.

18 in

26 in

30 in

30 in

Triangle A

26 in

Triangle B

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