Question

Jill traced the. three shapes shown out of cardboard for an art project. Select all of the shapes that will give Jill a piece of cardboard with the same total area. Please help!

Answer 1

1st and 3rd figures have the same area

Explanation:

1st figure is combined figure consisting of 4 m by 5 m rectangle and right triangle with legs

`4-1=3\ m` and
`10-5=5\ m`

The area of the first figure is

`A_(rectangle)=4* 5=20\ m^2\\ \\A_(triangle )=(1)/(2)\cdot 3\cdot 5=7.5\ m^2\\ \\A_(1^(st)\ figure)=20+7.5=27.5\ m^2`

2nd figure is combined figure consisting of 3 m by 6 m rectangle and right triangle with legs

3 m and
`1+3+1=5\ m`

The area of the second figure is

`A_(rectangle)=3* 6=18\ m^2\\ \\A_(triangle )=(1)/(2)\cdot 3\cdot 5=7.5\ m^2\\ \\A_(2^(nd)\ figure)=18+7.5=25.5\ m^2`

3rd figure is combined figure consisting of 10 m by 2 m rectangle and right triangle with legs

3 m and
`10-5=5\ m`

The area of the third figure is

`A_(rectangle)=2* 10=20\ m^2\\ \\A_(triangle )=(1)/(2)\cdot 3\cdot 5=7.5\ m^2\\ \\A_(3^(rd)\ figure)=20+7.5=27.5\ m^2`