INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

April 4, 2020

Area of Triangle Problem | AMC-8, 2019 | Problem 21

Try this beautiful problem from Geometry based on the area of the triangle.

Area of Triangle - AMC-8, 2019- Problem 21


What is the area of the triangle formed by the lines $y=5$, $y=1+x$, and $y=1-x$

  • $8$
  • $ 16$
  • $15$

Key Concepts


Geometry

Triangle

Linear equation

Check the Answer


Answer: $16$

AMC-8 (2019) Problem 21

Pre College Mathematics

Try with Hints


Find the three vertex of the triangle

Can you now finish the problem ..........

The area of the Triangle =\(\frac{1}{2} \times \{x_1(y_2 - y_3)+x_2(y+3 -y_1)+x_3(y_1 -y_2)\}\)

can you finish the problem........

Area of the triangle

Solving two The lines y=5 and y=1+x are intersect at (4,5)=\((x_1,y_1)\)(say)

Solving two The lines y=5 and y=1-x are intersect at (-4,5)=\((x_2,y_2)\)(say)

Solving two The lines y=1-x and y=1+x are intersect at (0,1)=\((x_1,y_1)\)(say)

Then the area of Triangle =\(\frac{1}{2} \times\{ x_1(y_2 - y_3)+x_2(y+3 -y_1)+x_3(y_1 -y_2)\}\)

= \(\frac{1}{2} \times \{4(5-1)+(-4)(1-5)+0(5-5)=\frac{1}{2} (16+16)=16\}\)

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com