Similar Figures: Calculate Area MPNO Given ABCD Area=1848

AAABBBCCCDDDEEEPPPMMMNNNOOOQQQ72.8 ONMP∼ABCD ONMP∼\text{ABCD}

DE = 7

OQ = 2.8

If the area of ABCD is 1848, then what is the area MPNO?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the area of MPNO
00:03 Similar polygons according to given data
00:10 The ratio of areas equals the square of the similarity ratio
00:22 Substitute appropriate values and solve to find the area
00:32 Multiply by the reciprocal to isolate the area
00:40 Square both numerator and denominator
00:45 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

AAABBBCCCDDDEEEPPPMMMNNNOOOQQQ72.8 ONMP∼ABCD ONMP∼\text{ABCD}

DE = 7

OQ = 2.8

If the area of ABCD is 1848, then what is the area MPNO?

2

Step-by-step solution

We are given that the triangles are similar, so we can compare the ratio between DE and OQ:

2.8:7

Raised to the 2nd power

7.84:49 7.84:49

We are given that the area of ABCD is 1848. Now we calculate the area of MPNO:

1848S=497.84 \frac{1848}{S}=\frac{49}{7.84}

S49=1848×7.84 S49=1848\times7.84

S49=14488.32 S49=14488.32

S=295.68 S=295.68

3

Final Answer

295.68

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