Question

find the area and perimeter of the triangle below. select the two answers that apply and round to the nearest tenth. (mark all correct answers) a. a = 12.5 b. a = 25 c. a = 10 d. p = 10 e. p = 16.2 f. p = 156.6

Explanation:

Step1: Calculate the base length

The two points on the base are $(-3,-1)$ and $(2,-1)$. Using the distance formula for points on a horizontal line (since $y$-coordinates are the same), the base $b=\vert2 - (-3)\vert= 5$.

Step2: Calculate the height

The height is the vertical distance from the vertex $(0,4)$ to the line $y = - 1$. So the height $h=\vert4-(-1)\vert = 5$.

Step3: Calculate the area

The area of a triangle formula is $A=\frac{1}{2}bh$. Substituting $b = 5$ and $h = 5$, we get $A=\frac{1}{2}\times5\times5=\frac{25}{2}=12.5$.

Step4: Calculate the lengths of the non - base sides

Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For the side connecting $(0,4)$ and $(-3,-1)$: $d_1=\sqrt{(0 + 3)^2+(4 + 1)^2}=\sqrt{9 + 25}=\sqrt{34}\approx5.8$.
For the side connecting $(0,4)$ and $(2,-1)$: $d_2=\sqrt{(0 - 2)^2+(4 + 1)^2}=\sqrt{4 + 25}=\sqrt{29}\approx5.4$.

Step5: Calculate the perimeter

The perimeter $P=b + d_1+d_2=5+5.8+5.4 = 16.2$.

Answer:

a. $A = 12.5$
e. $P=16.2$