Question

Rectangle ABCD is similar to rectangle WXYZ.24 in.wx6 in.BIf the area of WXYZ is 24 square inches, what is the area of ABCD?

Answer 1

Case: Similar shapes (Area of Rectangles)

Given:

Similar triangles ABCD and WXYZ.

|XY| = 6 in

Area of WXYZ = 24 sq in

|AD| = 24 in

Required: To find the Area of ABCD

Method:

Step 1: We find the length of side WX

`\begin{gathered} length* breadth\text{ = Area} \\ |XY\left|\text{ }*\right|WX\left|=\text{ 24}\right? \\ 6\text{ }*\left|WX\right|\text{ = 24} \\ |WX\left|\text{ =4 in}\right? \end{gathered}`

Step 2: Use similar sides to get the width |AB| of ABCD

Since the scale factor is 4 from WXYZ and ABCD

`\begin{gathered} |AB|\text{ = 1 }*4 \\ \left|AB\right?\left|=\text{ 4 in}\right? \end{gathered}`

Step 3: Now we find the Area of ABCD

`\begin{gathered} Area\text{ = \mid AB\mid }*\text{ \mid BD\mid} \\ Area\text{ = 24 }*\text{ 4} \\ Area\text{ = 96 sq in} \end{gathered}`

Final answer:

The area of ABCD is 96 sq in