Question

What is the area of the parallelogram?

20 √2 cm 2
40 cm 2
20 cm 2
40 √2 cm 2

Answer 1

20√2 cm²

Explanation:

Area of parallelogram = base * height

base (b) = 10 cm

height (h) = ?

Apply trigonometric function to find the height (h)

Assuming the height connecting the parallel bases together forms a right angle, therefore

Reference angle = 45°

Opposite = height (h)

Hypotenuse = 4 cm

Apply SOH:

Sin 45 = Opp/Hyp

Sin 45 = h/4

4*Sin 45 = h

4*√2/2 = h (sin 45 = √2/2)

2√2 = h

h = 2√2 cm

✔️Area = base * height = 10 * 2√2

= 20√2 cm²