Q15. - Geometry

Question

Find the area of each figure:

A ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ triangle with hypotenuse  10cm

Step-by-Step Solution

Answer

The area of given figure is $\frac{25\sqrt{3}}{2}$ square units.

Step 1. Given information.

Angles of a triangle are ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ with hypotenuse 10

Step 2. Analyze the figure.

Here, 

   $AC=2BC$    

 $\Rightarrow 10=2BC$

 $\Rightarrow BC=5$

 $$" width="9" height="19" style="max-width: none;" >$\Rightarrow b=BC=5$

       $AB=\sqrt{3}BC$ 

 

$\Rightarrow AB=\sqrt{3}\times 5$

$\Rightarrow AB=\sqrt{3}\times 5$

$\Rightarrow h=AB=5\sqrt{3}$

 

 

Step 3. Find the area of given figure.

The area of a triangle can be found using the formula

$A=\frac{1}{2}bh$

     $=\frac{1}{2}\times 5\times 5\sqrt{3}$

     $=\frac{25\sqrt{3}}{2}$Square units.

Therefore, the area of given figure is $\frac{25\sqrt{3}}{2}$square units.