Question

What is the area of this figure?

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Answer 1

42 units squared

Explanation:

break it up into smaller shapes. if you split the big shape at y = 2 and at y=-2, you'll get two triangles and one rectangle.

so the area of the rectangle = l x w

= 4 x 7

= 28

the area of the triangle is ( l x w )/2

= (7 x 2)/2

= 7

the other triangle is the same too

so the area of that is also 7.

now add all areas,

7+7+28 = 42

Answer 2

42 sq. units

Explanation:

I don't know if there's an easier way to do this but this is what I came up with. We can break this hexagon into 2 triangles and a rectangle (the 1st triangle using the top 3 points, the 2nd using the bottom 3, and the rectangle using the "middle" ones).

Rectangle area: 7*4 = 28

Triangles (they are equal) : 2*(1/2*7*2) = 14

28+14 = 42