Calculate Areas: Parallelograms with DC=10 and Height Constraint

ABCD and DCFE are forllel

It is known that:

DC=10 AE=8

Angle BAE equals 90 degrees

The height of the forllelogram ABCD for DC is less band 80% of the size of the side DC

Calculates the sum of the areas of the forllelograms.

101010888DDDAAABBBCCCEEEFFF

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Step-by-step video solution

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00:00 Calculate the sum of parallelogram areas
00:03 Opposite sides are parallel in parallelograms
00:09 Transitive property
00:18 Alternate angles sum to 180
00:25 Therefore this angle is also right
00:33 Opposite sides are equal in parallelograms
00:49 To find parallelogram area multiply height(H) by side(DC)
00:52 For each parallelogram multiply by its corresponding height (1,2)
01:00 Extract common factor
01:06 Sum of heights is the height itself (AE)
01:09 We'll substitute AE value and solve to find the areas
01:12 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

ABCD and DCFE are forllel

It is known that:

DC=10 AE=8

Angle BAE equals 90 degrees

The height of the forllelogram ABCD for DC is less band 80% of the size of the side DC

Calculates the sum of the areas of the forllelograms.

101010888DDDAAABBBCCCEEEFFF

3

Final Answer

80 cm²

Practice Quiz

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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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