Question

use appropriate formulas to find (a) the perimeter and (b) the area of the figure. (a) the perimeter is (type an integer or a decimal.)

Explanation:

Step1: Recall perimeter formula for trapezoid

$P=a + b+ c + d$, where $a,b,c,d$ are side - lengths. Here, assume the trapezoid has side - lengths $b = 5$ cm, $B = 8$ cm, and two non - parallel sides. Let's assume the non - parallel sides are $4.8$ cm each.
$P=4.8 + 5+4.8 + 8$

Step2: Calculate the sum

$P=(4.8+4.8)+(5 + 8)=9.6+13 = 22.6$ cm

Step3: Recall area formula for trapezoid

The area formula of a trapezoid is $A=\frac{(B + b)h}{2}$, where $B$ and $b$ are the lengths of the parallel sides and $h$ is the height. Given $B = 8$ cm, $b = 5$ cm, $h = 4$ cm.
$A=\frac{(8 + 5)\times4}{2}$

Step4: Simplify the area expression

First, calculate the sum inside the parentheses: $8 + 5=13$. Then, $\frac{13\times4}{2}=13\times2 = 26$ $cm^{2}$

Answer:

(a) The perimeter is $22.6$ cm
(b) The area is $26$ $cm^{2}$