Question

A trapezoid with an area of 3/4 cm^2 is dilated by a factor of 4.The area of the dilated trapezoid is ___ cm^2.

Answer 1

The area of the dilated trapezoid is 12 cm^2.​

Explanation:

We have that the formula for the area of a trapezoid is:

`A=((b+B))/(2)\cdot h`

The scale factor is 4, therefore we multiply each value by 4:

`\begin{gathered} A=((4b+4B))/(2)\cdot4h \\ A=(4(b+b))/(2)\cdot4h \\ A=4\cdot4\cdot((b+B))/(2)\cdot h \\ A=16\cdot((b+B))/(2)\cdot h \end{gathered}`

The area is known therefore it would remain:

`\begin{gathered} A=16\cdot(3)/(4) \\ A=12 \end{gathered}`