Question

What is the area of the scalene triangle shown (ABC), if AO = 10 cm, CO = 2 cm, BC = 5 cm, and AB = 12.20 cm? (Triangle AOB is a right triangle.)

Answer 1

The area of triangle ABC is
`25\ cm^(2)`

Explanation:

we know that

The area of triangle ABC is equal to the area of triangle ABO minus the area of triangle ACO

see the attached figure to better understand the problem

step 1

Find the area of triangle ABO

The area is equal to

`A=(1)/(2)(AO)(BO)`

substitute values

`A=(1)/(2)(10)(5+2)=35\ cm^(2)`

step 2

Find the area of triangle ACO

The area is equal to

`A=(1)/(2)(AO)(CO)`

substitute values

`A=(1)/(2)(10)(2)=10\ cm^(2)`

step 3

Find the area of triangle ABC

`35\ cm^(2)-10\ cm^(2)=25\ cm^(2)`