Question

What is the relationship between the area of ABCD and the area of EFGH? Quadrilateral ABCD with side measures 18 for AB, 24 for BC; quadrilateral EFGH with side measures 6 for EF, x for FG The ratio of the area of ABCD to the area of EFGH is 1:9. The ratio of the area of ABCD to the area of EFGH is 3:1. The ratio of the area of ABCD to the area of EFGH is 1:3. The ratio of the area of ABCD to the area of EFGH is 9:1.

Answer 1

The ratio of the area of ABCD to the area of EFGH is 9:1.

Explanation:

Let us assume that the shapes are rectangles and they are similar. If the two shapes are similar then their sides are in the same proportion. Therefore the ratio of the sides are in the same proportion.

`(AB)/(BC)=(EF)/(FG)\\ \\(18)/(24)=(6)/(x)\\\\18x=24*6\\ \\x=(24*6)/(18)=8`

The area of ABCD = AB × BC = 18 × 24 = 432

The area of EFGH = EF × FG = 6 × 8 = 48

The ratio of the area of ABCD to the area of EFGH = Area of ABCD / Area of EFGH = 432 / 48 = 9/1 = 9 : 1