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AMC 8 Geometry Math Olympiad USA Math Olympiad

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

Try this beautiful problem from Geometry: The area of triangle AMC-8, 2019. You may use sequential hints to solve the problem

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 =\(\frac{1}{2} \times\{ x_1(y_2 – y_3)+x_2(y+3 -y_1)+x_3(y_1 -y_2)\}\)

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

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