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

But try the problem first…

Answer: $16$

AMC-8 (2019) Problem 21

Pre College Mathematics

## Try with Hints

First hint

Find the three vertex of the triangle

Can you now finish the problem ……….

Second Hint

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……..

Final Step

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

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

## Other useful links

- https://www.cheenta.com/problem-from-probability-amc-8-2004problem-no-21/
- https://www.youtube.com/watch?v=aRevxA0u3D4

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