Question

find the measure of ∠d, and the perimeter and area of parallelogram abcd.
17 cm
28°
20 cm
8 cm
∠d = 62°, p = 37 centimeters, a = 160 square centimeters
∠d = 152°, p = 74 centimeters, a = 160 square centimeters
∠d = 62°, p = 37 centimeters, a = 340 square centimeters
∠d = 162°, p = 74 centimeters, a = 340 square centimeters

Explanation:

Step1: Find measure of ∠D

In a parallelogram, adjacent angles are supplementary. Given ∠A = 28°. So, ∠D=180° - ∠A.
∠D = 180°- 28° = 152°.

Step2: Find the perimeter P

In parallelogram ABCD, AB = CD = 17 cm and AD = BC = 20 cm. The perimeter formula for a parallelogram is P = 2(a + b) where a and b are adjacent - side lengths.
P=2(17 + 20)=2×37 = 74 cm.

Step3: Find the area A

The area formula for a parallelogram is A = base×height. Here, the base can be considered as AD = 20 cm and the height is 8 cm.
A = 20×8=160 cm².

Answer:

∠D = 152°, P = 74 centimeters, A = 160 square centimeters