Question

each unit on the coordinate grid represents 1 yard. the rectangular pool and triangular hot tub shown are both in need of covers. how much total material is needed to cover both? square yards

Explanation:

Step1: Calculate the area of the parallelogram (pool)

The formula for the area of a parallelogram is \(A = base\times height\).
From the grid, the base \(b = 6\) yards and the height \(h= 6\) yards.
\(A_{pool}=6\times6 = 36\) square yards.

Step2: Calculate the area of the right - triangle (hot tub)

The formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\).
From the grid, the base \(b = 3\) yards and the height \(h = 3\) yards.
\(A_{hot\ tub}=\frac{1}{2}\times3\times3=\frac{9}{2}=4.5\) square yards.

Step3: Calculate the total area

The total area \(A = A_{pool}+A_{hot\ tub}\).
\(A=36 + 4.5=40.5\) square yards.

Answer:

\(40.5\) square yards.