Question

find the area of the figure.

Explanation:

Step1: Identify base and height

The base of the large triangle is from $x = - 2$ to $x = 3$, so $b=5$. The height is from $y = 0$ to $y = 4$, so $h = 4$. The small triangle at the bottom has base from $x=0$ to $x = 1$, so $b_{1}=1$ and height $h_{1}=1$.

Step2: Calculate area of large triangle

The area formula for a triangle is $A=\frac{1}{2}bh$. For the large triangle, $A_{1}=\frac{1}{2}\times5\times4=10$.

Step3: Calculate area of small triangle

Using the area formula for a triangle, for the small triangle $A_{2}=\frac{1}{2}\times1\times1 = 0.5$.

Step4: Calculate area of the figure

The area of the figure $A = A_{1}-A_{2}=10 - 0.5=9.5$.

Answer:

$9.5$