Question

calculating the area of a composite figure
what is the area of the composite figure?
6
5
3
2
10
units²

Explanation:

Answer:

To find the area of the composite figure, we can calculate the area of the trapezoid and then subtract the area of the rectangular cut - out.

Step 1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A_{trapezoid}=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the two parallel sides and \(h\) is the height.
For the given trapezoid, \(a = 6\), \(b=10\) and \(h = 5\).
\[A_{trapezoid}=\frac{(6 + 10)\times5}{2}=\frac{16\times5}{2}=40\]

Step 2: Calculate the area of the rectangular cut - out

The formula for the area of a rectangle is \(A_{rectangle}=l\times w\), where \(l\) is the length and \(w\) is the width.
For the rectangular cut - out, \(l = 3\) and \(w=2\).
\[A_{rectangle}=3\times2 = 6\]

Step 3: Calculate the area of the composite figure

The area of the composite figure \(A\) is the area of the trapezoid minus the area of the rectangle.
\[A=A_{trapezoid}-A_{rectangle}=40 - 6=34\]

So the area of the composite figure is \(\boldsymbol{34}\) square units.