area of a composite figure. find the area of each figure, round your answer to the nearest whole number if necessary. 1) area:____ 2) area:____ 3) area:____ 4) area:____ 5) area:____ 6) area:____ 7) area:____ 8) area:____ 9) area:____

Question

Accepted Answer

1. **For the first figure**:
   - **Explanation**:
     - **Step 1: Split into two rectangles**
       - The top - rectangle has dimensions $36\ cm\times36\ cm$, and its area $A_1 = 36\times36= 1296\ cm^2$.
       - The bottom - rectangle has dimensions $60\ cm\times36\ cm$, and its area $A_2=60\times36 = 2160\ cm^2$.
     - **Step 2: Calculate total area**
       - The total area $A = A_1 + A_2=1296 + 2160=3456\ cm^2$.
2. **For the second figure**:
   - **Explanation**:
     - **Step 1: Split into a rectangle and a triangle**
       - The rectangle has dimensions $29\ ft\times10\ ft$, and its area $A_1=29\times10 = 290\ ft^2$.
       - The triangle has base $b = 29\ ft$ and height $h = 19\ ft$, and its area $A_2=\frac{1}{2}\times29\times19=\frac{551}{2}=275.5\ ft^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1 + A_2=290+275.5 = 565.5\approx566\ ft^2$.
3. **For the third figure**:
   - **Explanation**:
     - **Step 1: Split into two rectangles**
       - The left - rectangle has dimensions $4\ m\times2\ m$, and its area $A_1 = 4\times2=8\ m^2$.
       - The right - rectangle has dimensions $2\ m\times2\ m$, and its area $A_2 = 2\times2 = 4\ m^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1+A_2=8 + 4=12\ m^2$.
4. **For the fourth figure**:
   - **Explanation**:
     - **Step 1: Use the formula for the area of a trapezoid**
       - The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a = 5\ in$, $b = 10\ in$, and $h = 10\ in$.
       - $A=\frac{(5 + 10)\times10}{2}=\frac{15\times10}{2}=75\ in^2$.
5. **For the fifth figure**:
   - **Explanation**:
     - **Step 1: Split into a rectangle and a triangle**
       - The rectangle has dimensions $20\ yd\times12\ yd$, and its area $A_1=20\times12 = 240\ yd^2$.
       - The triangle has base $b = 12\ yd$ and height $h = 12\ yd$, and its area $A_2=\frac{1}{2}\times12\times12 = 72\ yd^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1+A_2=240 + 72=312\ yd^2$.
6. **For the sixth figure**:
   - **Explanation**:
     - **Step 1: Split into a rectangle and a triangle**
       - The rectangle has dimensions $16\ in\times12\ in$, and its area $A_1=16\times12 = 192\ in^2$.
       - The triangle has base $b = 8\ in$ and height $h = 12\ in$, and its area $A_2=\frac{1}{2}\times8\times12=48\ in^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1+A_2=192 + 48=240\ in^2$.
7. **For the seventh figure**:
   - **Explanation**:
     - **Step 1: Split into two rectangles**
       - The top - rectangle has dimensions $28\ yd\times28\ yd$, and its area $A_1=28\times28 = 784\ yd^2$.
       - The bottom - rectangle has dimensions $56\ yd\times14\ yd$, and its area $A_2=56\times14 = 784\ yd^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1+A_2=784+784 = 1568\ yd^2$.
8. **For the eighth figure**:
   - **Explanation**:
     - **Step 1: Split into two rectangles**
       - The left - rectangle has dimensions $21\ cm\times20\ cm$, and its area $A_1=21\times20 = 420\ cm^2$.
       - The right - rectangle has dimensions $18\ cm\times18\ cm$, and its area $A_2=18\times18 = 324\ cm^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1+A_2=420+324 = 744\ cm^2$.
9. **For the ninth figure**:
   - **Explanation**:
     - **Step 1: Split into two rectangles**
       - The left - rectangle has dimensions $9\ ft\times8\ ft$, and its area $A_1=9\times8 = 72\ ft^2$.
       - The right - rectangle has dimensions $6\ ft\times6\ ft$, and its area $A_2=6\times6 = 36\ ft^2$.
     - **Step 2: Calculate total area**
       - The total area $A=A_1+A_2=72+36 = 108\ ft^2$.

# Answer:
1. $3456\ cm^2$
2. $566\ ft^2$
3. $12\ m^2$
4. $75\ in^2$
5. $312\ yd^2$
6. $240\ in^2$
7. $1568\ yd^2$
8. $744\ cm^2$
9. $108\ ft^2$

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