Question

find the area of each figure. round your answer to 2 decimal places if required. (use $pi=3.14$)1)area = _____2)area = ___3)area = ___4)area = ___5)area = ___6)area = _____

Explanation:

1) Figure 1

Step1: Split into two rectangles

First rectangle: $16 \text{ yd} \times 4 \text{ yd}$; Second rectangle: $11 \text{ yd} \times 4 \text{ yd}$

Step2: Calculate each rectangle's area

Area 1: $16 \times 4 = 64$ $\text{yd}^2$; Area 2: $11 \times 4 = 44$ $\text{yd}^2$

Step3: Sum the two areas

$64 + 44 = 108$
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2) Figure 2

Step1: Recognize trapezoid formula

Area = $\frac{1}{2} \times (b_1 + b_2) \times h$, where $b_1=13\text{in}$, $b_2=7\text{in}$, $h=15\text{in}$

Step2: Substitute values into formula

$\frac{1}{2} \times (13 + 15) \times 15$

Step3: Compute the result

$\frac{1}{2} \times 28 \times 15 = 14 \times 15 = 210$ $\text{in}^2$
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3) Figure 3

Step1: Split into rectangle + triangle

Rectangle: $17\text{ft} \times (14-6)\text{ft}$; Triangle: $\frac{1}{2} \times 17\text{ft} \times 6\text{ft}$

Step2: Calculate rectangle area

$17 \times 8 = 136$ $\text{ft}^2$

Step3: Calculate triangle area

$\frac{1}{2} \times 17 \times 6 = 51$ $\text{ft}^2$

Step4: Sum the two areas

$136 + 51 = 187$ $\text{ft}^2$
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4) Figure 4

Step1: Split into rectangle + semicircle + triangle

Rectangle: $9\text{yd} \times 9\text{yd}$; Semicircle: $\frac{1}{2} \times \pi \times (\frac{9}{2})^2$; Triangle: $\frac{1}{2} \times 9\text{yd} \times 9\text{yd}$

Step2: Calculate rectangle area

$9 \times 9 = 81$ $\text{yd}^2$

Step3: Calculate semicircle area

$\frac{1}{2} \times 3.14 \times (\frac{9}{2})^2 = \frac{1}{2} \times 3.14 \times 20.25 = 31.7925$ $\text{yd}^2$

Step4: Calculate triangle area

$\frac{1}{2} \times 9 \times 9 = 40.5$ $\text{yd}^2$

Step5: Sum all areas

$81 + 31.7925 + 40.5 = 153.2925$ $\text{yd}^2$
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5) Figure 5

Step1: Split into rectangle + triangle, subtract notch

Rectangle: $19\text{in} \times 20\text{in}$; Triangle: $\frac{1}{2} \times 19\text{in} \times 8\text{in}$; Notch: $1\text{in} \times (20-8-1)\text{in}$

Step2: Calculate rectangle area

$19 \times 20 = 380$ $\text{in}^2$

Step3: Calculate triangle area

$\frac{1}{2} \times 19 \times 8 = 76$ $\text{in}^2$

Step4: Calculate notch area

$1 \times 11 = 11$ $\text{in}^2$

Step5: Compute total area

$380 + 76 - 11 = 445$ $\text{in}^2$
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6) Figure 6

Step1: Split into rectangle + trapezoid

Rectangle: $12\text{ft} \times 12\text{ft}$; Trapezoid: $\frac{1}{2} \times (12+5)\text{ft} \times (18-12)\text{ft}$

Step2: Calculate rectangle area

$12 \times 12 = 144$ $\text{ft}^2$

Step3: Calculate trapezoid area

$\frac{1}{2} \times 17 \times 6 = 51$ $\text{ft}^2$

Step4: Sum the two areas

$144 + 51 = 195$ $\text{ft}^2$

Answer:

1. $\boldsymbol{108 \text{ yd}^2}$
2. $\boldsymbol{210 \text{ in}^2}$
3. $\boldsymbol{187 \text{ ft}^2}$
4. $\boldsymbol{153.29 \text{ yd}^2}$
5. $\boldsymbol{445 \text{ in}^2}$
6. $\boldsymbol{195 \text{ ft}^2}$