Question

area - compound shapes
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: Calculate rectangle area

$A_{rect} = 12 \times 5 = 60$ in²

Step2: Calculate semicircle area

Radius $r = \frac{5}{2} = 2.5$ in
$A_{semi} = \frac{1}{2} \times 3.14 \times 2.5^2 = 9.8125$ in²

Step3: Sum the two areas

$A_{total} = 60 + 9.8125$

2) Figure 2

Step1: Split into rectangle + trapezoid

Rectangle: $7 \times 11 = 77$ ft²

Step2: Calculate trapezoid bases

Top base: $8$ ft, Bottom base: $20-7=13$ ft

Step3: Trapezoid area, sum total

$A_{trap} = \frac{1}{2} \times (8+13) \times 11 = 115.5$ ft²
$A_{total} = 77 + 115.5$

3) Figure 3

Step1: Split into kite + semicircle

Kite area: $\frac{1}{2} \times 10 \times 19 = 95$ yd²

Step2: Semicircle radius & area

Radius $r = \frac{13-7}{2} = 3$ yd
$A_{semi} = \frac{1}{2} \times 3.14 \times 3^2 = 14.13$ yd²

Step3: Sum the two areas

$A_{total} = 95 + 14.13$

4) Figure 4

Step1: Split into big square + small square

Big square: $16 \times 16 = 256$ in²

Step2: Small square area, sum total

Small square: $8 \times 8 = 64$ in²
$A_{total} = 256 + 64$

5) Figure 5

Step1: Split into square + parallelogram

Square: $9 \times 9 = 81$ ft²

Step2: Parallelogram dimensions & area

Base $9$ ft, Height $14-9=5$ ft
$A_{para} = 9 \times 5 = 45$ ft²

Step3: Sum the two areas

$A_{total} = 81 + 45$

6) Figure 6

Step1: Split into triangle + semicircle

Triangle area: $\frac{1}{2} \times 6 \times 4 = 12$ yd²

Step2: Semicircle radius & area

Radius $r = \frac{6}{2} = 3$ yd
$A_{semi} = \frac{1}{2} \times 3.14 \times 3^2 = 14.13$ yd²

Step3: Sum the two areas

$A_{total} = 12 + 14.13$

Answer:

1. $69.81$ in²
2. $192.50$ ft²
3. $109.13$ yd²
4. $320.00$ in²
5. $126.00$ ft²
6. $26.13$ yd²