Parallelogram Area Calculation: Using Perpendicular Heights BE=4 and BF=8

ABCD parallelogram, it is known that:

BE is perpendicular to DE

BF is perpendicular to DF

BF=8 BE=4 AD=6 DC=12

Calculate the area of the parallelogram in 2 different ways

121212666444888AAABBBCCCDDDEEEFFF

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find BE
00:05 To find the area of the parallelogram, multiply the height (FB) by side (AD)
00:10 Let's substitute appropriate values and solve for the area
00:16 Now let's use the same area formula to find the second height (BE)
00:20 Let's substitute appropriate values and solve for BE
00:29 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

ABCD parallelogram, it is known that:

BE is perpendicular to DE

BF is perpendicular to DF

BF=8 BE=4 AD=6 DC=12

Calculate the area of the parallelogram in 2 different ways

121212666444888AAABBBCCCDDDEEEFFF

2

Step-by-step solution

In this exercise, we are given two heights and two sides.

It is important to keep in mind: The external height can also be used to calculate the area

Therefore, we can perform the operation of the following exercise:

The height BF * the side AD

8*6

The height BE the side DC
4
*12

The solution of these two exercises is 48, which is the area of the parallelogram.

3

Final Answer

48 cm²

Practice Quiz

Test your knowledge with interactive questions

A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

6664.54.54.5

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