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.
A) <D = 62, P = 37 centimeters, A = 340 square centimeters
B) <D = 62, P = 37 centimeters, A = 160 square centimeters
C) <D=152, P = 74 centimeters, A = 160 square centimeters
D) <D=162, P = 74 centimeters, A = 340 square centimeters
To find the measure of angle D, we can use the fact that opposite angles in a parallelogram are congruent. Since angle A is 28 degrees, angle D is also 28 degrees.
To find the perimeter of the parallelogram, we can add up the lengths of all four sides. Side AB is given as 17 centimeters, and side AD is given as 20 centimeters. Since opposite sides of a parallelogram are congruent, side BC is also 17 centimeters and side CD is also 20 centimeters. Therefore, the perimeter is 17 + 20 + 17 + 20 = 74 centimeters.
To find the area of the parallelogram, we can multiply the base by the height. The base is the length of side AD, which is given as 20 centimeters. The height is given as 8 centimeters. Therefore, the area is 20 * 8 = 160 square centimeters.
Therefore, the correct answer is C) <D=152, P = 74 centimeters, A = 160 square centimeters.