 ## What is the Area of Triangle ?

The area of a Triangle is defined as the total space that is enclosed by any particular triangle. The basic formula to find the area of a given triangle is A = 1/2 × b × hwhere b is the base and h is the height of the given triangle, whether it is scalene, isosceles or equilateral. Also the area of Quadrilateral is defined as the half of the product of the length of the diagonals

## Try the problem from AMC 10 (2020)

Triangle AMC is isosceles with AM = AC. Medians $\overline {MV}$ and $\overline {CU}$ are perpendicular to each other, and $MV = CU =12$ . What is the area of $\triangle {AMC}$ ?

Source
Competency
Difficulty
Suggested Book

American Mathematics Competition 10 (AMC 10A), {2020}, {12}

Geometry – Area of Triangle

4 out of 10

Challenges and Thrills of Pre – College Mathematics

## Use some hints

First hint

We can imagine the portion $UVCM$ to be a quadrilateral having perpendicular diagonals .So its area can be found as half of the product of the length of the diagonals .

Second Hint

Again : – $\triangle AUV$ has $\frac {1}{4}$ of the triangle

$AMC$ by similarity.

So, $UVVM = \frac {3}{4} AMC$

Final Step

$\frac {1}{2} .12.12 = \frac {3}{4} AMC$

$72 = \frac {3}{4} AMC$

$AMC = 96$