Question

find the area of a triangle with one side of 57m. and the second side 46m. find the third side and the area​

Answer 1

Here to find the third side we need to assume that this triangle is a right angle triangle.

Let the given triangle be ∆ABC

here,

AB=57m

BC=46m

Angle B=90°

AC²=AB²+BC²

=57²+46²

=5365

$AC≈73.25m$

Area of ∆ABC=½×57×46

=57×23

$A(∆ABC)=1311m²$

Answer 2

Before, finding the answer. Let's find out how we can find the answer.

• Here, in this question, we have to find the third side first. To do that, we must use the Pythagoras theorem formula. And Pythagoras theorem :

$\boxed{ \tt Pyhagoras \: theorem = \sqrt{a^2 + b^2} }$

• Then, after finding the third side, we must find the area of the Triangle. So, to find the Area of the Triangle, we must use the formula of :

$\boxed{ \tt Area \: of \: Triangle = \frac{1}{2} \times b \times h }$

______________________

Given :

• Side one = 57 m
• Side two = 46 m

To find :

• third side and the area​

Solution :

$\tt Pyhagoras \: theorem = \sqrt{(Side)^2 + (Base)^2} }$

                               = √57² + 46²

                               = √3249 + 2116

                               = √5365

                               =  73.24 m

Now,

${ \tt Area \: of \: Triangle = \dfrac{1}{2} \times b \times h }$

                            ${ \tt = \dfrac{1}{2} \times 57 \times 46 }$

                            ${ \tt = \dfrac{1}{2} \times 2622 }$

                            ${ \tt = \dfrac{2622 }{2} }$

                            ${ \tt = 1311}$

Therefore, the Area of the Triangle is 1311 m².