Chauncey

Chauncey is building a storage bench for his son's playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chauncy wants to buy a triangular-shaped cover for the bench.

Suppose the storage bench is 2 1/2 ft along one wall and 4 1/4 ft along the other wall. How big will the cover have to be to cover the entire bench?

Correct answer:

A =  5 ⁵⁄₁₆ = 85/16 ft²

Step-by-step explanation:

$$\begin{gathered} a=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2.5\text{ft} \\ b=4\frac{1}{4}=4+\frac{1}{4}=\frac{4\cdot 4+1}{4}=\frac{16+1}{4}=\frac{17}{4}=4.25\text{ft} \\ A=\frac{1}{2}\cdot a\cdot b=\frac{1}{2}\cdot \frac{5}{2}\cdot \frac{17}{4}=\frac{85}{16}{\text{ft}}^2=5\frac{5}{16}{\text{ft}}^2=5.3125{\text{ft}}^2 \end{gathered}$$

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