Question

A composite figure is shown. A five-sided figure with two parallel bases. The top one is 4.6 inches. The vertical height between these bases is 3.15 inches. That vertical height intersects the bottom base, leaving 3.3 inches between it and the vertex to the left. The side on the right is the longest at 6.3 inches. There is a horizontal line connecting the vertex of the bottom base to the 6.3-inch side and that line is 3 inches. Which of the following represents the total area of the figure? 10.663 in2 24.413 in2 28.448 in2 34.335 in2

Answer 1

Answer: 24.413in^2

Explanation:

The figure can be broken into two triangles and two rectangles. To calculate the area of the composite figure, we will need to calculate the area of each individual shape and then add the results together.

To calculate the area of a triangle, we will use the formula A=1/2 bh, where b is the base and h is the height of the triangle.

For the triangle on the left, b = 3.3 inches and h = 3.15 inches. Plugging these values into the formula, we get A = 1/2 (3.3)(3.15) = 5.1975 square inches.

For the triangle on the right, b = (6.3-3.15) -> b=3.15 inches and h = 3 inches. Plugging these values into the formula, we get A = 1/2 (3.15)(3) = 4.725 square inches.

To calculate the area of a rectangle, we will use the formula A = lw, where l is the length and w is the width of the rectangle.

For the rectangle, l = 4.6 inches and w = 3.15 inches. Plugging these values into the formula, we get A = (4.6)(3.15) = 14.49 square inches.

Adding all of these results together, we get the total area of the figure:

5.1975+4.725+14.49 = 24.413 square inches

Answer 2

Area of the composite figure: (top base x height) +
(2 x area of a triangle) = (4.6 × 3.15) + (2 × (3.3 × 3)/2)
= 14.43 + 4.95 = 19.38 in2 + area of a trapezoid =
19.38 + (3.3 + 6.3 × 3)/2 = 19.38 + 12.15 = 24.413 in2