Question

7A painted design on a tile is composedof a square and two right triangles. Eachside of the square and the height of eachtriangle measure 4.5 inches. The base ofeach triangle measures 6 inches.What is the total area of the painteddesign in square inches?10212(3 (3)4400100OOO212(3 (3)(414 (4)515 (5 56 (6 (6) 6W0100(8)818 (8) (8)919 ( (9 9©(8)8(9

Answer 1

There are two different shapes in the iamge, the first is a rectangle and the second is a triangle. To determine the area of each of these, we need to use the following expressions:

`\begin{gathered} A_{\text{square}}=side^2 \\ A_(triangle)=(b\cdot h)/(2) \end{gathered}`

Since there are two triangles, the total area of the image is:

`A=A_{\text{square}}+2\cdot A_{\text{triangle}}`

So we need to calculate the area of each shape first. This is done below:

`\begin{gathered} A_{\text{square}}=4.5^2=20.25\text{ square inches} \\ A_{\text{triangle}}=(4.5\cdot6)/(2)=13.5\text{ square inches} \end{gathered}`

Now we can calculate the total area:

`A=20.25+2\cdot13.5=47.25\text{ square inches}`

The total area is 47.25 square inches