area of a polygon in a unit grid

Geometry Level 1

Find the area of the polygon in the unit grid shown.


The answer is 18.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The polygon shown is a trapezoid. And the area is given by A = 1 2 ( a + b ) h A=\dfrac{1}{2}(a+b)h where a a and b b are the bases and h h is the height. So the area is

A = 1 2 ( 3 + 6 ) ( 4 ) = 18 A=\dfrac{1}{2}(3+6)(4)=\boxed{18}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

You can also split it (mentally) into a 3 by 4 rectangle and 2 triangles with a combined base of 3 and height of 4. 3 * 4 + (3 * 4)/2 = 12 + 6 = 18.

Denton Young - 2 years, 10 months ago

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