Question

Find the measure of D, and the perimeter and area of parallelogram ABCD. Parallelogram A B C D is shown. Side A B is 17 centimeters. Side A D is 20 centimeters. Angle A is 28 degrees. The height is 8 centimeters.

Answer 1

ABCD is 74 centimeters, and the area is 160 square centimeters.

Explanation:

To find the measure of angle D in parallelogram ABCD, we can use the fact that opposite angles in a parallelogram are congruent. Since angle A is given as 28 degrees, angle D will also measure 28 degrees.

To find the perimeter of parallelogram ABCD, we can add the lengths of all four sides. Given that side AB is 17 centimeters and side AD is 20 centimeters, we can use the fact that opposite sides of a parallelogram are congruent. Therefore, the perimeter is:

Perimeter = 2(AB + AD) = 2(17 + 20) = 2(37) = 74 centimeters.

To find the area of parallelogram ABCD, we can multiply the base (side AD) by the height. The base AD is given as 20 centimeters and the height is given as 8 centimeters. Therefore, the area is:

Area = base × height = 20 × 8 = 160 square centimeters.

So, the measure of angle D is 28 degrees, the perimeter of parallelogram ABCD is 74 centimeters, and the area is 160 square centimeters.