Question

exercises 15 - 18
in exercises 15 - 18, determine (a) the area and (b) the perimeter of the figure.

1. 11 mi 9 mi
2. 5 m 3 m 6 m 3 m 5 m
3. 12 in. 9 in. 7 in.
4. 3 km 4 km

Explanation:

Exercise 15

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is $A = l\times w$, where $l = 11$ mi and $w=9$ mi. So $A=11\times9 = 99$ square - miles.

Step2: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is $P=2(l + w)$. Substitute $l = 11$ mi and $w = 9$ mi, we get $P=2(11 + 9)=2\times20=40$ miles.

Step1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a = 6$ m, $b=3 + 6+3=12$ m and $h$ (the height) can be found using the Pythagorean theorem. The non - parallel sides are 5 m and the base difference is $12 - 6=6$ m, so the height $h = 4$ m. Then $A=\frac{(6 + 12)\times4}{2}=\frac{18\times4}{2}=36$ square meters.

Step2: Calculate the perimeter of the trapezoid

The perimeter $P=5 + 6+5+(3 + 6+3)=28$ m.

Step1: Calculate the area of the parallelogram

The formula for the area of a parallelogram is $A = b\times h$, where $b = 12$ in and $h = 7$ in. So $A=12\times7=84$ square inches.

Step2: Calculate the perimeter of the parallelogram

The opposite sides of a parallelogram are equal. The sides are 9 in and 12 in, so the perimeter $P = 2(9+12)=2\times21 = 42$ inches.

Answer:

(a) 99 square - miles
(b) 40 miles

Exercise 16