Question

There is a pair of parallel sides in the following shape. 4 4 6 What is the area of the shape?​

Answer 1

Answer: 20

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Step-by-step explanation:

It might help to rotate the figure so the parallel sides are horizontal. This is optional.

The parallel bases are
`b_1 = 6` and
`b_2 = 4` in either order.

The height is h = 4 which is always perpendicular to both bases.

Plug these values into the trapezoid area formula.

`A = (h(b_1 + b_2))/(2)\\\\A = (4(6+4))/(2)\\\\A = (4(10))/(2)\\\\A = (40)/(2)\\\\A = 20\\\\`

The area of the trapezoid is 20 square units.

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Another pathway is to break the trapezoid into a rectangle up top and a triangle down below.

The rectangle is 4 by 4 with area 4*4 = 16

The triangle has a base of 6-4 = 2 and height of 4, so its area is base*height/2 = 2*4/2 = 8/2 = 4

Overall the total area is rectangle+triangle = 16+4 = 20 square units.