Question

Determine the area of the shaded regions in the figures below. Write the final polynomial in standard form

Answer 1

for the tringle:

area=
`p^(2) -2p-3`

for the frame:

area=
`8x+28`

Explanation:

For the tringle:-

Area=1/2bh

Area=1/2(2p-6)(p+1)

Area=1/2(
`2p^(2) -4p-6`)

Area=
`p^(2) -2p-3`

For the picture frame:-

part 1:the area of the big frame

Area=lw

Area=(x+7)(x+4)

Area=
`x^(2) +11x+28`

part 2:the area of the small frame

Area=lw

Area=(x+3)(x)

Area=
`x^(2) +3x`

To find the area of the shaded regions:

Area of shaded region=area of the big frame-the area of the small frame

Area of shaded region=
`(x^(2) +11x+28)-(x^(2) +3x)`

Area of shaded region=
`8x+28`