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?
what is the area of the shaded trapezoid?
what is the area of the shaded region?

Explanation:

Step1: Calculate the area of the shaded right - triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). For the right - triangle, \(b = 4\) in and \(h=(6 - 4)=2\) in.
\(A_1=\frac{1}{2}\times4\times2=\frac{1}{2}\times8 = 4\) sq.in.

Step2: Calculate the area of the shaded trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\). Here, \(a=(6 - 3)=3\) in, \(b = 6\) in, and \(h=(4 - 2)=2\) in.
\(A_2=\frac{(3 + 6)\times2}{2}=\frac{9\times2}{2}=9\) sq.in.

Step3: Calculate the total area of the shaded region

Add the areas of the two shaded parts (\(A = A_1+A_2\)).
\(A=4 + 9=13\) sq.in.

Answer:

What is the area of the shaded right - triangle? \(4\) sq.in.
What is the area of the shaded trapezoid? \(9\) sq.in.
What is the area of the shaded region? \(13\) sq.in.