Question

Geometry Find the area of the triangle shown.

Short answer

The area of the given triangle is $12x+4$.

Step-by-step solution

Step-1 – Distributive property

For any real numbers a, b, and c, the distributive property is given by:

$a\left(b+c\right)=a·b+a·c$

Step-2 – Area of triangle formula

The area of a triangle with base length b and height h is given by the formula

$\text{Area of triangle}=\frac{1}{2}·b·h$

Step-3 – Find area of given triangle

In the given triangle observe that the base length is 8 units and height of the triangle is $3x+1$.

So, substitute these values of base and height in the above formula of area of tringle and simplify further as shown below

$\begin{array}{c}\text{Areaoftriangle}=\frac{1}{2}\cdot b\cdot h\\ =\frac{1}{2}\cdot 8\cdot (3x+1)\\ =4(3x+1)\\ =4\cdot \left(3x\right)+4\cdot 1\\ =12x+4\end{array}$

Thus, the area of the given triangle is $12x+4$.