A quadrilateral with sides 8 cm, 9 cm, 6 cm, and 5 cm has area 45 cm^2 . Find the area of a simi

step 1 Okay, this is problem number 15. It says that a quadrilateral with sides 8 centimeters, 9 centim

A quadrilateral with sides 8 cm, 9 cm, 6 cm, and 5 cm has...

A quadrilateral with sides $8 \mathrm{cm}, 9 \mathrm{cm}, 6 \mathrm{cm},$ and 5 $\mathrm{cm}$ has area 45 $\mathrm{cm}^{2}$ . Find the area of a similar quadrilateral whose longest side is 15 $\mathrm{cm} .$

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Key Concepts

Similarity of Geometric Figures

This concept refers to figures that have the same shape but differ in size. When figures are similar, all corresponding angles are equal and the ratios of corresponding sides are constant. This shared property allows the application of proportionate reasoning in solving problems related to dimensions and areas.

Linear Scale Factor

The linear scale factor is the ratio between any pair of corresponding lengths in two similar figures. It is a crucial element when comparing geometric properties such as side lengths, perimeters, and distances. The scale factor directly influences the calculation of other measures in similar figures.

Area Scaling in Similar Figures

In similar figures, areas scale by the square of the linear scale factor. This means if the lengths in one figure are multiplied by a scale factor k to produce a similar figure, the area of the new figure will be multiplied by k². This relationship is fundamental in problems where the areas of similar shapes are compared based on changes in their linear dimensions.

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