Question

a triangle has a base of 2^3 units and a height of 2^4 units. what is the area of the triangle? write your answer as a power of 2. (type your answer using exponential notation)

Explanation:

Step1: Recall area formula for triangle

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. Given $b = 2^{3}$ and $h=2^{4}$.

Step2: Substitute values into formula

$A=\frac{1}{2}\times2^{3}\times2^{4}$. Since $\frac{1}{2}=2^{- 1}$, then $A = 2^{-1}\times2^{3}\times2^{4}$.

Step3: Use exponent - rule for multiplication

According to the rule $a^{m}\times a^{n}=a^{m + n}$, we have $A=2^{-1 + 3+4}$.

Step4: Calculate the exponent

$-1 + 3+4=6$. So $A = 2^{6}$.

Answer:

$2^{6}$