Question

solving a real - world problem
carter is building a model sailboat. the boat will have two triangular sails. one sail will have a base of 24 inches and a
height of 56 inches. the other sail will have a base of 14 inches and a height of 33 inches. what is the minimum amount
of material carter needs to build the sails?
1, 806 inches²
903 inches²
672 inches²
1, 344 inches²

Explanation:

Step1: Calculate the area of the first sail

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). For the first sail with \(b = 24\) inches and \(h=56\) inches, we substitute into the formula:
\(A_1=\frac{1}{2}\times24\times56\)
\(A_1 = 12\times56\)
\(A_1=672\) square inches.

Step2: Calculate the area of the second sail

For the second sail with \(b = 14\) inches and \(h = 33\) inches, using the formula \(A=\frac{1}{2}bh\):
\(A_2=\frac{1}{2}\times14\times33\)
\(A_2=7\times33\)
\(A_2 = 231\) square inches.

Step3: Find the total area of the two sails

The total area \(A=A_1 + A_2\).
\(A=672+231\)
\(A = 903\) square inches.

Answer:

\(903\) inches\(^{2}\)