A composite figure is comprised of a rectangle and two congruent right triangle on either side. The triangle have a height of 4 inches and a width of 3 inches.
The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite
To find the area of the rectangle within the composite figure, we first need to find the total area of the composite figure.
The total area of the composite figure is the sum of the area of the rectangle and the two congruent right triangles.
Area of a rectangle = length x width
Area of a rectangle = x(3)
Area of a rectangle = 3x
Area of a triangle = (1/2) x base x height
Area of a triangle = (1/2) x 3 x 4
Area of a triangle = 6
Total area of the composite figure = 3x + 2(6)
Total area of the composite figure = 3x + 12
Given that the total area of the composite figure is 40 square inches:
3x + 12 = 40
3x = 28
x = 9.33
Therefore, the area of the rectangle within the composite figure is:
Area of the rectangle = 3x = 3(9.33) = 27.99 square inches.