Question

the tabletop below is made from right triangles, each the same size. your company charges $0.20 per square inch for sanding the tabletop. which of the following is closest to the tabletops area, in square inches? a. 550 b. 950 c. 2,800 d. 3,950 e. 5,600

Explanation:

Step1: Calculate the area of one right - triangle

The formula for the area of a right - triangle is \(A=\frac{1}{2}bh\). Here, \(b = 20\) inches and \(h=20\) inches. So, \(A_{triangle}=\frac{1}{2}\times20\times20= 200\) square inches.

Step2: Count the number of right - triangles

By counting the number of right - triangles in the octagonal table - top, we find there are \(14\) right - triangles.

Step3: Calculate the area of the table - top

The area of the table - top \(A = 14\times A_{triangle}\). Substitute \(A_{triangle}=200\) into the formula: \(A=14\times200 = 2800\) square inches.

Answer:

C. \(2,800\)