Question

Two consecutive sides of a parallelogram measure 32 centimeters and 15 centimeters. The angle made by the pair of consecutive sides is 135°. What is the area of the parallelogram?

A. 16.6 square centimeters
B. 339.4 square centimeters
C. 169.7 square centimeters
D. 678.8 square centimeters

Answer 1

1) Find the height (h) of the parallelogram,
angle made by the pair of consecutive sides is ---- >135°=180°-135°=45°

B=32
sin 45 = h/15

h = (15√2)/2 cm

so
Area of parallelogram=B*h
Area of parallelogram = (32) * (15√2)/2 = 240√2 cm^2 ≈ 339.411 cm^2

The answer is the option B. 339.4 square centimeters