Question

Rex has a square deck that is 9 feet long on each side. He decides to add triangular benches in each corner as is shown in the diagram. What is the area of the deck that is not covered by benches?

Answer 1

area of square=9 ft × 9ft= 81 ft²

area of one triangle= 1/2 ×3²=4.5ft²
4.5ft²×4=18ft²

remaining area= 81ft²-18ft²=63ft²

Answer 2

Answer: The answer is 63 square feet.

Step-by-step explanation:  Given that Rex has a square deck of 9 feet length on each side. He decides to add triangular benches in each corner as shown in the diagram. We are to find the area of the deck which is not covered by the benches.

As shown in the figure, each of the four benches will make a right-angled triangle of base 3 feet and altitude 3 feet.

So, the area of each triangle will be

$T=\dfrac{1}{2}\times 3\times 3=4.5~\textup{square feet}.$

Now, the area of the square deck is

$S=9\times 9=81~\textup{square feet}.$

Since there are four triangular benches at each corner of the deck, so the area of the deck that is not covered by the benches is given by

$A_nb=S-T=81-4\times 4.5=81-18=63~\textup{square feet}.$

Thus, the answer is 63 square feet.