SOLUTION:
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
[tex]\begin{gathered} length\times breadth\text{ = Area} \\ |XY\left|\text{ }\times\right|WX\left|=\text{ 24}\right? \\ 6\text{ }\times\left|WX\right|\text{ = 24} \\ |WX\left|\text{ =4 in}\right? \end{gathered}[/tex]
Step 2: Use similar sides to get the width |AB| of ABCD
Since the scale factor is 4 from WXYZ and ABCD
[tex]\begin{gathered} |AB|\text{ = 1 }\times4 \\ \left|AB\right?\left|=\text{ 4 in}\right? \end{gathered}[/tex]
Step 3: Now we find the Area of ABCD
[tex]\begin{gathered} Area\text{ = \mid AB\mid }\times\text{ \mid BD\mid} \\ Area\text{ = 24 }\times\text{ 4} \\ Area\text{ = 96 sq in} \end{gathered}[/tex]
Final answer:
The area of ABCD is 96 sq in
