Calculate Parallelogram Area: 7cm Height with Connected Isosceles Triangle

Triangle BDE an isosceles

DEFA parallelogram FC=6

Point E divides BC by 2:3 (BE>EC)

The height of the trapezoid DEFA for the side AF is equal to 7 cm

Calculate the area of the parallelogram DEFA

666777DDDEEEFFFAAACCCBBB

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Step-by-step video solution

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00:21 Let's find the area of parallelogram, D-E-F-A. Alright?
00:27 Remember, in a parallelogram, opposite sides are parallel.
00:32 A side parallel to one line, is also parallel to that line's extension.
00:38 Also, corresponding angles between parallel lines are the same. Keep that in mind.
00:46 Once more, opposite sides are parallel in a parallelogram.
00:51 And, corresponding angles between these lines are equal.
01:06 Now, let's talk about the transversal rule.
01:15 The triangles here are similar by the A-A-A rule, meaning, angle-angle-angle.
01:22 Find the similarity ratio by dividing the matching sides.
01:28 Put in the given values to find D-E. Alright, let's do that.
01:33 Next, we need to isolate D-E. Almost there!
01:37 And this gives us the length of side D-E.
01:42 To find the area of the parallelogram, multiply height, H, by side, D-E.
01:48 Substitute the values and solve to find the area.
01:53 And that's how we solve the problem. Great job!

Step-by-step written solution

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1

Understand the problem

Triangle BDE an isosceles

DEFA parallelogram FC=6

Point E divides BC by 2:3 (BE>EC)

The height of the trapezoid DEFA for the side AF is equal to 7 cm

Calculate the area of the parallelogram DEFA

666777DDDEEEFFFAAACCCBBB

3

Final Answer

63 cm².

Practice Quiz

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Calculate the area of the parallelogram according to the data in the diagram.

101010777AAABBBCCCDDDEEE

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