Question

for exercises 1-4, find the area of the given trapezoid.
1.
2.
3.
4.
reinforce understanding
49

Explanation:

Step1: Recall trapezoid area formula

The area of a trapezoid is given by:
$$A=\frac{1}{2}(b_1 + b_2)h$$
where $b_1, b_2$ are the two parallel bases, and $h$ is the height (perpendicular distance between the bases).

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Problem 1:

Step1: Identify bases and height

Top base $b_1=10\ \text{m}$, bottom base $b_2=1+10+1=12\ \text{m}$, height $h=9\ \text{m}$

Step2: Substitute into formula

$$A=\frac{1}{2}(10 + 12)\times9=\frac{1}{2}\times22\times9=99\ \text{m}^2$$

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Problem 2:

Step1: Identify bases and height

Top base $b_1=4\ \text{in}$, bottom base $b_2=6\ \text{in}$, height $h=7\ \text{in}$

Step2: Substitute into formula

$$A=\frac{1}{2}(4 + 6)\times7=\frac{1}{2}\times10\times7=35\ \text{in}^2$$

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Problem 3:

Step1: Identify bases and height

Top base $b_1=7\ \text{ft}$, bottom base $b_2=7+6=13\ \text{ft}$, height $h=6\ \text{ft}$

Step2: Substitute into formula

$$A=\frac{1}{2}(7 + 13)\times6=\frac{1}{2}\times20\times6=60\ \text{ft}^2$$

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Problem 4:

Step1: Identify bases and height

Top base $b_1=1+5+3=9\ \text{m}$, bottom base $b_2=5\ \text{m}$, height $h=2\ \text{m}$

Step2: Substitute into formula

$$A=\frac{1}{2}(9 + 5)\times2=\frac{1}{2}\times14\times2=10\ \text{m}^2$$

Answer:

1. $99\ \text{m}^2$
2. $35\ \text{in}^2$
3. $60\ \text{ft}^2$
4. $10\ \text{m}^2$