find the area of each trapezoid.
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7. the area of a trapezoid is 84 ft². the bases are 4 ft and 10 ft. find the height.
8. the area of a trapezoid is 60 m². the bases are 8 m and 16 m. find the height.

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1. **For the general formula of the area of a trapezoid**:
   - The formula for the area of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1$ and $b_2$ are the lengths of the bases and $h$ is the height.
2. **Problem 1**:
   - Given $b_1 = 5\mathrm{ft}$, $b_2=9\mathrm{ft}$, and $h = 4\mathrm{ft}$.
   - # Explanation:
     - ## Step 1: Add the bases
       - $b_1 + b_2=5 + 9=14\mathrm{ft}$
     - ## Step 2: Multiply by height and divide by 2
       - $A=\frac{(b_1 + b_2)h}{2}=\frac{14\times4}{2}=28\mathrm{ft}^2$
   - # Answer: $28\mathrm{ft}^2$
3. **Problem 2**:
   - Given $b_1 = 6\mathrm{m}$, $b_2 = 10\mathrm{m}$, and $h=15\mathrm{m}$.
   - # Explanation:
     - ## Step 1: Add the bases
       - $b_1 + b_2=6 + 10 = 16\mathrm{m}$
     - ## Step 2: Multiply by height and divide by 2
       - $A=\frac{(b_1 + b_2)h}{2}=\frac{16\times15}{2}=120\mathrm{m}^2$
   - # Answer: $120\mathrm{m}^2$
4. **Problem 3**:
   - Given $b_1 = 5\mathrm{m}$, $b_2 = 17\mathrm{m}$, and $h = 3\mathrm{m}$.
   - # Explanation:
     - ## Step 1: Add the bases
       - $b_1 + b_2=5+17 = 22\mathrm{m}$
     - ## Step 2: Multiply by height and divide by 2
       - $A=\frac{(b_1 + b_2)h}{2}=\frac{22\times3}{2}=33\mathrm{m}^2$
   - # Answer: $33\mathrm{m}^2$
5. **Problem 4**:
   - Given $b_1 = 7\mathrm{cm}$, $b_2 = 11\mathrm{cm}$, and $h = 3\mathrm{cm}$.
   - # Explanation:
     - ## Step 1: Add the bases
       - $b_1 + b_2=7 + 11=18\mathrm{cm}$
     - ## Step 2: Multiply by height and divide by 2
       - $A=\frac{(b_1 + b_2)h}{2}=\frac{18\times3}{2}=27\mathrm{cm}^2$
   - # Answer: $27\mathrm{cm}^2$
6. **Problem 5**:
   - Given $b_1 = 8\mathrm{ft}$, $b_2 = 12\mathrm{ft}$, and $h = 5\mathrm{ft}$.
   - # Explanation:
     - ## Step 1: Add the bases
       - $b_1 + b_2=8 + 12 = 20\mathrm{ft}$
     - ## Step 2: Multiply by height and divide by 2
       - $A=\frac{(b_1 + b_2)h}{2}=\frac{20\times5}{2}=50\mathrm{ft}^2$
   - # Answer: $50\mathrm{ft}^2$
7. **Problem 6**:
   - Given $b_1 = 4\mathrm{m}$, $b_2 = 21\mathrm{m}$, and $h = 7\mathrm{m}$.
   - # Explanation:
     - ## Step 1: Add the bases
       - $b_1 + b_2=4+21 = 25\mathrm{m}$
     - ## Step 2: Multiply by height and divide by 2
       - $A=\frac{(b_1 + b_2)h}{2}=\frac{25\times7}{2}=87.5\mathrm{m}^2$
   - # Answer: $87.5\mathrm{m}^2$
8. **Problem 7**:
   - Given $A = 84\mathrm{ft}^2$, $b_1 = 4\mathrm{ft}$, $b_2 = 10\mathrm{ft}$.
   - # Explanation:
     - ## Step 1: First, use the area - formula $A=\frac{(b_1 + b_2)h}{2}$, and re - arrange it to solve for $h$. We get $h=\frac{2A}{b_1 + b_2}$.
     - ## Step 2: Add the bases
       - $b_1 + b_2=4 + 10=14\mathrm{ft}$
     - ## Step 3: Calculate the height
       - $h=\frac{2\times84}{14}=12\mathrm{ft}$
   - # Answer: $12\mathrm{ft}$
9. **Problem 8**:
   - Given $A = 60\mathrm{m}^2$, $b_1 = 8\mathrm{m}$, $b_2 = 16\mathrm{m}$.
   - # Explanation:
     - ## Step 1: Re - arrange the area formula $A=\frac{(b_1 + b_2)h}{2}$ to $h=\frac{2A}{b_1 + b_2}$
     - ## Step 2: Add the bases
       - $b_1 + b_2=8 + 16=24\mathrm{m}$
     - ## Step 3: Calculate the height
       - $h=\frac{2\times60}{24}=5\mathrm{m}$
   - # Answer: $5\mathrm{m}$

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