Question

sam created a porch that was part wooden and part concrete, as shown in the figure below. note: figure not drawn to scale. if a = 21 ft, b = 28 ft, and c = 35 ft, what is the total area of the porch? assume that the wooden part is a right triangle and the concrete part is a square. a. 217 ft² b. 119 ft² c. 1,519 ft² d. 1,715 ft²

Explanation:

Step1: Calculate area of right - triangle

The area formula for a right - triangle is $A_{triangle}=\frac{1}{2}ab$. Given $a = 21$ ft and $b = 28$ ft, then $A_{triangle}=\frac{1}{2}\times21\times28=\frac{1}{2}\times588 = 294$ ft².

Step2: Calculate area of square

The area formula for a square is $A_{square}=c^{2}$. Given $c = 35$ ft, then $A_{square}=35^{2}=1225$ ft².

Step3: Calculate total area

The total area of the porch $A = A_{triangle}+A_{square}$. So $A=294 + 1225=1519$ ft².

Answer:

C. 1,519 ft²