A simple area

Geometry Level 1

What is the area of a triangle with vertices at ( 0 , 0 ) , ( 0 , 6 ) (0,0), (0, 6) and ( 3 , 3 ) (3, 3) ?


The answer is 9.

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2 solutions

Denton Young
Mar 17, 2016

Draw a straight line from (0, 0) to (0, 6). This is the triangle's base. It has a length of 6.

Now drop a perpendicular to this from (3, 3). It has a length of 3. This is the triangle's height.

Area of triangle = 1/2 * base * height = 1/2 * 3 * 6 = 9

Moderator note:

Simple standard approach. Sometimes it can be hard to find a suitable base and height.

By using matrix,,,,,we can do it... [ 0 0 1 0 6 1 3 3 1 ] \begin{bmatrix} 0 & 0 & 1 \\ 0 & 6 & 1 \\ 3 & 3 & 1\end{bmatrix}

Next step [ 0 6 3 3 ] \begin{bmatrix} 0 & 6 \\ 3 & 3\end{bmatrix}

So →( 0 × 3 0 \times 3 ) + ( 6 × 3 6 \times 3 ) =0+18=18

So, the area of that triangle 0.5*18=9(Ans)

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