What is the area of the parallelogram?

20 √2 cm 2
40 cm 2
20 cm 2
40 √2 cm 2

20√2 cm²

Step-by-step 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

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.