Question

First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces. Then find the area of the divisions. A 7-sided figure has a rectangle at one end and a triangle at the other end. The height of the triangle is 4 meters. The length and height of the triangle are 3 and 4 meters. A square in between has 4 meters length and height.

Answer 1

The total area of the given figure is 34 square meter.

Explanation:

The total area of the given figure is 34 square meter.The figure can be divided into two triangles and one rectangle. The triangle at one end is 3 m long and 4 m high, while the triangle at the other end has a base of 4 m and a height of 3 m. The rectangle in between has a length and width of 4 m.The total area of the triangles is 1/2 ×Base×Height= 1/2×3×4 + 1/2×4×3 = 18 m²The total area of the rectangles is 4 × 4 = 16 m²The total area of the figure is 18 + 16 = 34 m²Therefore, the total area of the given figure is 34 square meter.