Question

directions - use the diagram of a trapezoid to find the following: a) perimeter = in. b) area = in.

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a trapezoid is the sum of the lengths of its four - sides. Given side lengths \(KJ = 4\) in, \(JI=5\) in, \(IH = 7\) in, \(HK = 5\) in.
\[P=KJ + JI+IH + HK\]

Step2: Calculate the perimeter

\[P=4 + 5+7 + 5=21\] in.

Step3: Recall area formula

The area \(A\) of a trapezoid is given by the formula \(A=\frac{(b_1 + b_2)h}{2}\), where \(b_1\) and \(b_2\) are the lengths of the parallel sides and \(h\) is the height. Here, \(b_1 = 4\) in, \(b_2 = 7\) in, and \(h = 4\) in.
\[A=\frac{(4 + 7)\times4}{2}\]

Step4: Calculate the area

First, calculate the sum of the parallel sides: \(4 + 7=11\) in. Then, multiply by the height and divide by 2. \(A=\frac{11\times4}{2}=22\) in².

Answer:

a) 21 in.
b) 22 in².