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 × h, where 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
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 \(\triangle {AMC}\) ?
American Mathematics Competition 10 (AMC 10A), {2020}, {12}
Geometry - Area of Triangle
4 out of 10
Challenges and Thrills of Pre - College Mathematics
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 .
Again : - \(\triangle AUV \) has \(\frac {1}{4}\) of the triangle
\(AMC \) by similarity.
So, \(UVVM = \frac {3}{4} AMC \)
\(\frac {1}{2} .12.12 = \frac {3}{4} AMC \)
\(72 = \frac {3}{4} AMC \)
\(AMC = 96 \)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
You havee mentioned above:
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 × h, where 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
You should correct : last line that is :Also the area of Quadrilateral is defined as the half of the product of the length of the diagonals, It should be (1/2)* the product of the length of the diagonals* sin of angle between Two diagonols;
In the example it clicked because Angle between Two Diagonals=90°& Sin 90°=1;
Thank you for going through my post. In this sum as i am using the area of quadrilateral as =1/2 of the product of the length of the diagonals so in competency i have mentioned whatever i have used in the problem.I got your point but as triangle is the main focus here so i haven't mentioned the angle part in are of quadrilateral. Once again thank you.