Question

Can you help me out with a question

Answer 1

The composite shape shown in the picture can be divided into three forms:

1) An equilateral triangle with side length a=22ft

The area of an equilateral triangle can be determined using the following formula:

`A_1=\frac{a^2\sqrt[]{3}}{4}`

Replace it with a=22ft

`\begin{gathered} A_1=\frac{22^2\sqrt[]{3}}{4} \\ A_1=\frac{484\sqrt[]{3}}{4} \\ A_1=209.58ft^2 \end{gathered}`

2) A square with side length a=22ft

The area of the square can be determined as the square of the side length:

`\begin{gathered} A_2=a^2 \\ A_2=22^2 \\ A_2=484ft^2 \end{gathered}`

3) A triangle with height 22ft and base 16ft

The area of the triangle can be calculated as half the product of the base and the height:

`\begin{gathered} A_3=(1)/(2)bh \\ A_3=(1)/(2)22\cdot16 \\ A_3=176ft^2 \end{gathered}`

The total area of the composite shape is equal to the sum of the three areas:

`\begin{gathered} TA=A_1+A_2+A_3 \\ TA=209.58+484+176 \\ TA=869.58ft^2 \end{gathered}`