find area of parallelogram

Question

How do i find the area of a parallelogram if i know the perimeter and two heights?

Answer 1

All you need to know is the exact base and height. The base I will call (side b) is just going to be one of the sides given. And the height is exactly perpendicular to the base meaning it forms a 90 degree angle with the side you chose. The height I will call (h) is just drawn from the (side b) to the other side that also equals (side b) and makes a 90 degree angle between (side b) and (h)

(Essentially you are making the parallelogram into a rectangle which is easy to find its area with sides of the rectangle being (side b) and (h))

Use trig formulas to figure out the height using (adjacent side) which is the (side b)

The (adjacent side)= c , (side b)= a, and (h)= b where a,b,c are the sides you are familiar with to the right triangle where (a^2)+(b^2)=(c^2)

Then the area will be (base b)(h) which is your answer

Answer 2

Hi. The area of the parallelogram is base x height. If you already know the height, you only need the base to get the answer.

However, you notice that when you see the height drawn to the base, a right triangle is formed. You need to use the formula a squared + b squared = c squared to find the side of the parallelogram. Since you know the perimeter, and can subtract the 2 sides (which are equal), you will get the base.

Then multiply base x height, and you arrive at your answer.