Question

chapter quiz
find the perimeter of each figure.

1. 12 m 10 m 10 m
2. 53 ft 39 ft 3 ft 9 ft 56 ft 30 ft
3. 15 in. 13 in. 10 in. 18 in.

find the area of each figure.

1. 30 mm 8 mm
2. 56 cm
3. 6 ft 4 ft 19 ft

find the value of x in each diagram.

1. 22 yd 12 yd 19 yd p = 73 yd x
2. 21 m area = 147 m² x
3. area = 169 mm² x

Explanation:

Step1: Calculate perimeter of triangle in question 1

Perimeter of a triangle is sum of side - lengths. So, $P = 12+10 + 10=32$ m.

Step2: Calculate perimeter of figure in question 2

$P=39 + 53+30 + 9+56=187$ ft.

Step3: Calculate perimeter of figure in question 3

$P=13 + 15+10 + 18=56$ in.

Step4: Calculate area of rectangle in question 4

Area of rectangle $A = l\times w$, so $A=30\times8 = 240$ mm².

Step5: Calculate area of square in question 5

Area of square $A = s^2$, so $A = 56\times56=3136$ cm².

Step6: Calculate area of trapezoid in question 6

Area of trapezoid $A=\frac{(a + b)h}{2}$, where $a = 6$, $b = 19$, $h = 4$. So $A=\frac{(6 + 19)\times4}{2}=\frac{25\times4}{2}=50$ ft².

Step7: Find $x$ in question 7

Given perimeter $P$ of trapezoid, $P=x + 19+12 + 22$. Since $P = 73$ yd, then $x+19 + 12+22=73$, $x=73-(19 + 12+22)=20$ yd.

Step8: Find $x$ in question 8

Area of parallelogram $A = base\times height$. Given $A = 147$ m² and height $h = 21$ m, then $147=x\times21$, $x=\frac{147}{21}=7$ m.

Step9: Find $x$ in question 9

Area of square $A = x^2$. Given $A = 169$ mm², then $x^2=169$, $x = 13$ mm.

Answer:

1. Perimeter: 32 m
2. Perimeter: 187 ft
3. Perimeter: 56 in
4. Area: 240 mm²
5. Area: 3136 cm²
6. Area: 50 ft²
7. $x = 20$ yd
8. $x = 7$ m
9. $x = 13$ mm