Question

name copy each drawing onto a separate sheet of paper and then calculate the area of the figure. 1) 1 in 1 in 2) 6.9 in 2.4 in 3) 5.9 in 4 in 4) 14.2 cm 10.2 cm 10.2 cm 5) 18 mi 18 mi 6) 19 in 19 in 7) 4.5 mi 8 mi 8) 6.6 yd 7 yd 9) 14 m 8 m 7 m 16 m 10) 2 in 2 in 4 in 11) 1.5 in 2.9 in 3.3 in 12) 13.6 km 6.7 km 6 km 5.2 km 6.4 km 13) 4.5 m 14) 5 cm 15) 26 cm 16) 3 m 6.5 m

Explanation:

Step1: Recall area formulas

• Area of square: $A = s^2$ (where $s$ is side - length).
• Area of rectangle: $A=l\times w$ (where $l$ is length and $w$ is width).
• Area of parallelogram: $A = b\times h$ (where $b$ is base and $h$ is height).
• Area of triangle: $A=\frac{1}{2}\times b\times h$ (where $b$ is base and $h$ is height).
• Area of trapezoid: $A=\frac{1}{2}(a + b)h$ (where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height).
• Area of circle: $A=\pi r^2$ (where $r$ is the radius).

Step2: Calculate areas one - by - one

1) Square with $s = 1$ in

$A = 1\times1=1$ in²

2) Rectangle with $l = 6.9$ in and $w = 2.4$ in

$A=6.9\times2.4 = 16.56$ in²

3) Parallelogram with $b = 5.9$ in and $h = 4$ in

$A=5.9\times4=23.6$ in²

4) Rectangle with $l = 14.2$ cm and $w = 10.2$ cm

$A=14.2\times10.2 = 144.84$ cm²

5) Square with $s = 18$ mi

$A=18\times18=324$ mi²

6) Square with $s = 19$ in

$A=19\times19 = 361$ in²

7) Triangle with $b = 8$ mi and $h = 4.5$ mi

$A=\frac{1}{2}\times8\times4.5=18$ mi²

8) Triangle with $b = 7$ yd and $h = 6.6$ yd

$A=\frac{1}{2}\times7\times6.6 = 23.1$ yd²

9) Triangle with $b = 16$ m and $h = 7$ m

$A=\frac{1}{2}\times16\times7=56$ m²

10) Trapezoid with $a = 2$ in, $b = 4$ in and $h = 2$ in

$A=\frac{1}{2}(2 + 4)\times2=6$ in²

11) Trapezoid with $a = 1.5$ in, $b = 3.3$ in and $h = 2.9$ in

$A=\frac{1}{2}(1.5+3.3)\times2.9=\frac{1}{2}\times4.8\times2.9 = 6.96$ in²

12) Trapezoid with $a = 6.4$ km, $b = 13.6$ km and $h = 5.2$ km

$A=\frac{1}{2}(6.4 + 13.6)\times5.2=\frac{1}{2}\times20\times5.2=52$ km²

13) Circle with $r = 4.5$ m

$A=\pi\times(4.5)^2=\pi\times20.25\approx3.14\times20.25 = 63.585$ m²

14) Circle with $r = 5$ cm

$A=\pi\times5^2=25\pi\approx25\times3.14 = 78.5$ cm²

15) Circle with $d = 26$ cm, so $r = 13$ cm

$A=\pi\times13^2=\pi\times169\approx3.14\times169 = 530.66$ cm²

16) Parallelogram with $b = 6.5$ m and $h = 3$ m

$A=6.5\times3=19.5$ m²

Answer:

1. 1 in²
2. 16.56 in²
3. 23.6 in²
4. 144.84 cm²
5. 324 mi²
6. 361 in²
7. 18 mi²
8. 23.1 yd²
9. 56 m²
10. 6 in²
11. 6.96 in²
12. 52 km²
13. 63.585 m²
14. 78.5 cm²
15. 530.66 cm²
16. 19.5 m²