Question

find the area of each figure.
1.
2.
3.
4.
5.
6.
find the area of the shaded region in each figure.

1. yard with a sandbox

yard – 15 ft by 20 ft
sandbox – 6 ft by 7 ft

1. wall with windows

wall – 8 ft by 16 ft
each window – 5 ft by 4 ft

1. sidewalk around pool

sidewalk – 30 ft by 30 ft
pool – 27 ft by 27 ft

1. a bedroom is 15 ft long and 12 ft wide. how much will it cost to carpet the room if carpeting costs $22 per square yard? (1 yd = 3 ft)
2. a rose garden in the city park is rectangular and is 9 m wide. if the area of the rectangle is 144 m², what is the length of the garden?

Explanation:

Step1: Calculate area of rectangle

$A_1 = 6 \times 4 = 24$ $\text{m}^2$

Step2: Split into 2 rectangles, calculate sum

$A_2 = (6 \times 4) + (2 \times 2) = 24 + 4 = 28$ $\text{m}^2$

Step3: Subtract cutout from big rectangle

$A_3 = (6 \times 4) - (3 \times 2) = 24 - 6 = 18$ $\text{m}^2$

Step4: Split into 2 rectangles, calculate sum

$A_4 = (8 \times 6) + (5 \times (10-6)) = 48 + 20 = 68$ $\text{in}^2$

Step5: Split into 2 rectangles, calculate sum

$A_5 = (12 \times 7) + (7 \times (12-7)) = 84 + 35 = 119$ $\text{in}^2$

Step6: Split into 2 rectangles, calculate sum

$A_6 = (18 \times 5) + (9 \times (10-5)) = 90 + 45 = 135$ $\text{cm}^2$

Step7: Subtract sandbox from yard

$A_7 = (15 \times 20) - (6 \times 7) = 300 - 42 = 258$ $\text{ft}^2$

Step8: Subtract 2 windows from wall

$A_8 = (8 \times 16) - 2\times(5 \times 4) = 128 - 40 = 88$ $\text{ft}^2$

Step9: Subtract pool from sidewalk area

$A_9 = (30 \times 30) - (27 \times 27) = 900 - 729 = 171$ $\text{ft}^2$

Step10: Find area, convert to yards, calculate cost

Room area: $15 \times 12 = 180$ $\text{ft}^2$
Convert to yards: $\frac{180}{9} = 20$ $\text{yd}^2$
Total cost: $20 \times 22 = 440$ dollars

Step11: Solve for length using area formula

Length $l = \frac{144}{9} = 16$ $\text{m}$

Answer:

1. $\boldsymbol{24\ \text{m}^2}$
2. $\boldsymbol{28\ \text{m}^2}$
3. $\boldsymbol{18\ \text{m}^2}$
4. $\boldsymbol{68\ \text{in}^2}$
5. $\boldsymbol{119\ \text{in}^2}$
6. $\boldsymbol{135\ \text{cm}^2}$
7. $\boldsymbol{258\ \text{ft}^2}$
8. $\boldsymbol{88\ \text{ft}^2}$
9. $\boldsymbol{171\ \text{ft}^2}$
10. $\boldsymbol{\$440}$
11. $\boldsymbol{16\ \text{m}}$