Question 980584
The height of the triangle is one leg of a right triangle with the 30 side as hypotenuse and 1/2 the 10 side as the other leg:
A=short leg=5; B=height; C=hypotenuse=30
{{{A^2+B^2=C^2}}}
.
{{{B^2=C^2-A^2}}}
.
{{{B=sqrt(C^2-A^2)}}}
{{{B=sqrt(30^2-5^2)}}}
{{{B=sqrt(875)}}}
{{{B=5sqrt(35)}}}
.
Area=1/2 x base x height
{{{Area=(1/2)x10x5sqrt(35)}}}
{{{Area=25sqrt(35)}}}
Area =147.9 square units