Question

What is the area of the parllelogtam shown below

Answer 1

Answer: 16 square units

Let x be the height of the parallelogram. Right now it's unknown, but we can solve for it using the pythagorean theorem. Focus on the right triangle. It has legs a = 3 and b = x, with hypotenuse c = 5

a^2 + b^2 = c^2

3^2 + x^2 = 5^2

9 + x^2 = 25

x^2 = 25-9

x^2 = 16

x = sqrt(16)

x = 4

This is a 3-4-5 right triangle.

The height of the parallelogram is 4 units.

We have enough info to find the area of the parallelogram

Area of parallelogram = base*height

Area of parallelogram = 4*4

Area of parallelogram = 16 square units

Coincidentally, the base and height are the same, which isn't always going to be the case. The base is visually shown as the '4' in the diagram. The height is the dashed line, which also happens to be 4 units long.