Similar Figures: Calculate Area MPNO Given ABCD Area=1848

Question

$ONMP∼\text{ABCD}$

DE = 7

OQ = 2.8

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

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

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

$7.84:49$

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

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

$S49=1848\times7.84$

$S49=14488.32$

$S=295.68$

295.68