Question

A trapezoid is broken into 2 triangles and 1 rectangle. The triangles both have a base of 2 meters and a height of 5 meters. The rectangle has a height of 5 meters and a width of 2 meters. A kite is broken into 2 triangles each with a height of 3 meters and a base of 7 meters.

The trapezoid and kite have been broken for you.
The trapezoid has an area of m2.
The kite has an area of m2.
The area of the trapezoid is the area of the kite.

Answer 1

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Answer

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1 - B

2 - C

3 - C

Proof

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Answer 2

Part 1) The trapezoid has an area of
`20\ m^2`

Part 2) The kite has an area of
`21\ m^2`

Part 3) The area of the trapezoid is less than the area of the kite

Explanation:

Part 1

Find the area of trapezoid

we know that

The area of trapezoid is equal to the area of two congruent triangles plus the area of a rectangle

so

`A=2[(1)/(2) (2)(5)]+(2)(5)`

`A=10+10=20\ m^2`

Part 2

Find the area of the kite

we know that

The area of the kite is equal to the area of two congruent triangles

so

`A=2[(1)/(2) (7)(3)]=21\ m^2`

Part 3

Compare the areas

The trapezoid has an area of
`20\ m^2`

The kite has an area of
`21\ m^2`

so

`20\ m^2< 21\ m^2`

therefore

The area of the trapezoid is less than the area of the kite