Question

the end views of two different barns are shown. without calculating, decide which end has the greater area. explain how you know. a. the end of barn 1 has a greater area because the triangular part has a greater height than that of the triangular part of the end of barn 2, while they both have the same base. b. the end of barn 2 has a greater area because it has the longest vertical side, though barn 1 is taller. c. the end of barn 2 has a greater area because both the triangular and rectangular parts have greater areas than the corresponding parts for barn 1. d. the end of barn 1 has a greater area because the rectangular part has a greater width than that of the rectangular part of the end of barn 2, while they both have the same length.

Explanation:

The area of a triangle is calculated as \(A=\frac{1}{2}\times base\times height\). For the triangular parts of the barns, both have the same base (the width of the barn, which is 72 for both). The height of the triangular part of Barn 1 is 60, and the height of the triangular part of Barn 2 is 48. Since \(60>48\), and the base is the same, the area of the triangular part of Barn 1 is larger. The rectangular parts of both barns have the same width (72) and height (72), so their areas are equal. So, the total area of the end of Barn 1 (area of rectangle + area of triangle) is larger than that of Barn 2.

Answer:

A. The end of Barn 1 has a greater area because the triangular part has a greater height than that of the triangular part of the end of Barn 2, while they both have the same base.