Question

activity 1 - area of composite figures
question #4 - 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?
8 sq. in.
what is the area of the shaded region?
14 sq. in.

Explanation:

Step1: Calculate the area of the rectangle

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

Step2: Calculate the area of the un - shaded right - triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). The base \(b=(6 - 4)=2\) in and the height \(h = 3\) in. So, \(A_{triangle1}=\frac{1}{2}\times2\times3= 3\) sq.in.

Step3: Calculate the area of the un - shaded trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)}{2}\times h\). Here, \(a = 2\) in, \(b = 4\) in and \(h=(6 - 3)=3\) in. So, \(A_{trapezoid}=\frac{(2 + 4)}{2}\times3=9\) sq.in.

Step4: Calculate the area of the shaded region

The area of the shaded region \(A = A_{rectangle}-A_{triangle1}-A_{trapezoid}\). Substitute the values: \(A=24-(3 + 9)=24 - 12=12\) sq.in.

Answer:

12 sq.in.