Area of a triangle

Geometry Level 2

In the unit grid shown below, what is the area of the triangle?


The answer is 11.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Relevant wiki: General Polygons - Area

The area of the triangle is equal to the area of the square minus the area of the 3 3 yellow triangles.

A = 5 2 − 1 2 ( 2 ) ( 4 ) − 1 2 ( 3 ) ( 5 ) − 1 2 ( 1 ) ( 5 ) = 25 − 4 − 15 2 − 5 2 = 50 2 − 8 2 − 15 2 − 5 2 = 22 2 = A=5^2-\dfrac{1}{2}(2)(4)-\dfrac{1}{2}(3)(5)-\dfrac{1}{2}(1)(5)=25-4-\dfrac{15}{2}-\dfrac{5}{2}=\dfrac{50}{2}-\dfrac{8}{2}-\dfrac{15}{2}-\dfrac{5}{2}=\dfrac{22}{2}= 11 \boxed{11}

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