Question

activity 1 - area of composite figures
question 6d - determine the area of the shaded region in each figure.
what is the area of the shaded right triangle? 6 sq. in.
what is the area of the shaded trapezoid? 18 in.
what is the area of the shaded region? 10 sq. in.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = length\times width\). Here, \(length = 6\) in and \(width = 4\) in. So, \(A_{rectangle}=6\times4 = 24\) sq in.

Step2: Calculate the area of the un - shaded trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 2\) in, \(b = 4\) in, and \(h=(6 - 2)=4\) in. Then \(A_{trapezoid}=\frac{(2 + 4)\times2}{2}+\frac{(2 + 4)\times2}{2}=6 + 6=12\) sq in.

Step3: Calculate the area of the shaded region

Subtract the area of the un - shaded trapezoid from the area of the rectangle. \(A_{shaded}=A_{rectangle}-A_{trapezoid}\). So, \(A_{shaded}=24- 12=12\) sq in.

Answer:

The area of the shaded region is \(12\) square inches.