Question

calculator
this figure is made up of a triangle and a semicircle.
what is the area of the figure?
use 3.14 for π.
enter your answer, as a decimal, in the box.
units²

Explanation:

Step1: Find the area of the triangle

The formula for the area of a triangle is \(A_{\text{triangle}}=\frac{1}{2}\times b\times h\).
From the graph, we can use the distance formula or count the units. The base \(b = 4\) units and the height \(h=4\) units.
So, \(A_{\text{triangle}}=\frac{1}{2}\times4\times4 = 8\)

Step2: Find the area of the semicircle

The formula for the area of a circle is \(A_{\text{circle}}=\pi r^{2}\). For a semicircle, \(A_{\text{semicircle}}=\frac{1}{2}\pi r^{2}\).
The diameter of the semicircle is \(4\) units (from \(x = 0\) to \(x = 4\) on the \(x -\)axis), so the radius \(r = 2\) units.
Using \(\pi=3.14\), we have \(A_{\text{semicircle}}=\frac{1}{2}\times3.14\times2^{2}=\frac{1}{2}\times3.14\times4=6.28\)

Step3: Find the total area

The total area \(A = A_{\text{triangle}}+A_{\text{semicircle}}\)
\(A=8 + 6.28=14.28\)

Answer:

\(14.28\)