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Before continuing, make sure you understand the main points of this lesson:
- A triangle is half of a parallelogram. The formula to find a triangle's area is [tex]A=\frac{1}{2} b \cdot h[/tex].
- A trapezoid has one pair of parallel sides. The formula for finding the area of a trapezoid is [tex]A=\frac{1}{2}\left(b_1+b_2\right) \cdot h[/tex].
- Measurements must have common units before calculating area.
- To find a missing measurement, substitute the information you are given into the area equation and solve for what is missing.

Practice finding the area of triangles and trapezoids by completing the following exercise:

1. Find the height of a triangle that has an area of [tex]27 \text{ ft}^2[/tex] and a base of 9 ft.
- [ ] 243 ft
- [ ] 6 ft
- [ ] 121.5 ft

2. Find the area of a trapezoid that has bases of 4 cm and 5 cm, and a height of 3 cm.
- [ ] [tex]$13.5 \text{ cm}^2$[/tex]
- [ ] [tex]$30 \text{ cm}^2$[/tex]
- [ ] [tex]$27 \text{ cm}^2$[/tex]
- [ ] [tex]$6 \text{ cm}^2$[/tex]

3. Find the height of a trapezoid that has bases of 9 yd and 12 yd, and an area of 21 square yards.
- [ ] 5 yd
- [ ] 220.5 yd
- [ ] 1 yd
- [ ] 2 yd



Answer :

GinnyAnswer
Sure, let's break down each part of the question step-by-step.

### 1. Finding the Height of a Triangle
We are given:
- Area of the triangle, [tex]\( A = 27 \, \text{ft}^2 \)[/tex]
- Base of the triangle, [tex]\( b = 9 \, \text{ft} \)[/tex]

The formula for the area of a triangle is:
[tex]\[ A = \frac{1}{2} b \cdot h \][/tex]

To find the height ([tex]\( h \)[/tex]), we can rearrange the formula:
[tex]\[ h = \frac{2A}{b} \][/tex]

Substitute the given values:
[tex]\[ h = \frac{2 \cdot 27}{9} = \frac{54}{9} = 6 \, \text{ft} \][/tex]

So, the height of the triangle is [tex]\( 6 \, \text{ft} \)[/tex].

The choices were:
- [tex]\( 243 \, \text{ft} \)[/tex]
- [tex]\( 6 \, \text{ft} \)[/tex] (Correct choice)
- [tex]\( 121.5 \, \text{ft} \)[/tex]

### 2. Finding the Area of a Trapezoid
We are given:
- First base of the trapezoid, [tex]\( b_1 = 4 \, \text{cm} \)[/tex]
- Second base of the trapezoid, [tex]\( b_2 = 5 \, \text{cm} \)[/tex]
- Height of the trapezoid, [tex]\( h = 3 \, \text{cm} \)[/tex]

The formula for the area of a trapezoid is:
[tex]\[ A = \frac{1}{2} (b_1 + b_2) \cdot h \][/tex]

Substitute the given values:
[tex]\[ A = \frac{1}{2} (4 + 5) \cdot 3 = \frac{1}{2} \cdot 9 \cdot 3 = \frac{27}{2} = 13.5 \, \text{cm}^2 \][/tex]

So, the area of the trapezoid is [tex]\( 13.5 \, \text{cm}^2 \)[/tex].

The choices were:
- [tex]\( 13.5 \, \text{cm}^2 \)[/tex] (Correct choice)
- [tex]\( 30 \, \text{cm}^2 \)[/tex]
- [tex]\( 27 \, \text{cm}^2 \)[/tex]
- [tex]\( 6 \, \text{cm}^2 \)[/tex]

### 3. Finding the Height of a Trapezoid
We are given:
- First base of the trapezoid, [tex]\( b_1 = 9 \, \text{yd} \)[/tex]
- Second base of the trapezoid, [tex]\( b_2 = 12 \, \text{yd} \)[/tex]
- Area of the trapezoid, [tex]\( A = 21 \, \text{square yards} \)[/tex]

The formula for the height of a trapezoid is:
[tex]\[ h = \frac{2A}{b_1 + b_2} \][/tex]

Substitute the given values:
[tex]\[ h = \frac{2 \cdot 21}{9 + 12} = \frac{42}{21} = 2 \, \text{yd} \][/tex]

So, the height of the trapezoid is [tex]\( 2 \, \text{yd} \)[/tex].

The choices were:
- [tex]\( 5 \, \text{yd} \)[/tex]
- [tex]\( 220.5 \, \text{yd} \)[/tex]
- [tex]\( 1 \, \text{yd} \)[/tex]
- [tex]\( 2 \, \text{yd} \)[/tex] (Correct choice)

To summarize:
1. The height of the triangle is [tex]\( 6 \, \text{ft} \)[/tex].
2. The area of the trapezoid is [tex]\( 13.5 \, \text{cm}^2 \)[/tex].
3. The height of the trapezoid is [tex]\( 2 \, \text{yd} \)[/tex].

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