Q15. - Algebra 1

Question

Write an expression that describes the area in square units of a triangle with a height of $4c^3{d}^2$ and a base of $3c{d}^4$.

 

Step-by-Step Solution

Answer

The area of a triangle is $\mathbf{6}{\mathit{c}}^4{\mathit{d}}^6$ square units.

Step 1. The formula for the area of a triangle.

An area of a triangle is given by

 $$\begin{gathered} A=\frac{1}{2}\cdot base\cdot height \\ =\frac{1}{2}\cdot b\cdot h \end{gathered}$$

Step 2. Substitution.

Substitute $4c^3{d}^2$ for $h$ and $3c{d}^4$ for $b$ into $A=\frac{1}{2}\cdot b\cdot h$.

$A=\frac{1}{2}\cdot \left(3c{d}^4\right)\cdot \left(4c^3{d}^2\right)$

Step 3. Simplify.

Simplify the above-obtained equation.

$$\begin{gathered} A=\frac{1}{2}\cdot 12c^4{d}^6 \\ =6c^4{d}^6 \end{gathered}$$

Therefore, the area of a triangle $6c^4{d}^6$ is square units.