Question

Uyen measures two rectangular tabletops. The green tabletop has dimensions of 7 feet by 4 1/2feet. The area of the brown tabletop is 1 1/2 times as great as the area of the green tabletop. What is the area of the brown tabletop?

Answer 1

We have that the area of the brown tabletop is given by the following expression:

$A_b=1\frac{1}{2}\cdot A_g$

Let's find first the area of the green tabletop. If the base measures 7 feet and the height is 4 1/2 feet, then:

$\begin{gathered} A_g=b\cdot h_{} \\ \Rightarrow A_g=(7)\cdot(4\frac{1}{2})=7\cdot(\frac{9}{2})=\frac{63}{2}=31\frac{1}{2} \\ A_g=31\frac{1}{2}ft^2 \end{gathered}$

now that we know the area of the green tabletop, we can find the area of the brown tabletop:

$\begin{gathered} A_b=1\frac{1}{2}\cdot A_g \\ A_g=31\frac{1}{2} \\ \Rightarrow A_b=1\frac{1}{2}\cdot(31\frac{1}{2})=(\frac{3}{2})(\frac{63}{2})=\frac{189}{4}=47\frac{1}{4} \\ A_b=47\frac{1}{4}ft^2 \end{gathered}$

therefore, the area of the brown tabletop is 47 1/4 ft^2