Question

1. find the area of the triangle below. use the formula (a=\frac{1}{2}bh). write in the simplest radical form. (sqrt{12}) (10sqrt{8}) (5sqrt{2})

Explanation:

Step1: Identify base and height

Let the base $b = 5\sqrt{2}$ and height $h=\sqrt{12}$.

Step2: Simplify the square - root terms

We know that $\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$.

Step3: Apply the area formula

The area formula of a triangle is $A=\frac{1}{2}bh$. Substitute $b = 5\sqrt{2}$ and $h = 2\sqrt{3}$ into the formula:
$A=\frac{1}{2}\times5\sqrt{2}\times2\sqrt{3}$.

Step4: Calculate the product

First, $\frac{1}{2}\times5\times2 = 5$. Then, $\sqrt{2}\times\sqrt{3}=\sqrt{6}$ according to the rule $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$. So $A = 5\sqrt{6}$.

Answer:

$5\sqrt{6}$