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. click on the icon to view area formulas for several shapes. (type cubic units square units units exponential notation)

Explanation:

Step1: Recall triangle - area formula

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

Step2: Substitute given values

Given $b = 2^{3}$ and $h=2^{4}$. Then $A=\frac{1}{2}\times2^{3}\times2^{4}$.
Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $2^{3}\times2^{4}=2^{3 + 4}=2^{7}$. And $\frac{1}{2}=2^{- 1}$. So $A = 2^{-1}\times2^{7}$.

Step3: Simplify using exponent rule

Again, using $a^{m}\times a^{n}=a^{m + n}$, we get $A=2^{-1 + 7}=2^{6}$.

Answer:

$2^{6}$ square units