Question

Lori creates the following design for a T-shirt.

Lori found the areas of Triangle 1 and Rectangle 1. Find the areas of the remaining figures.

The area of Rectangle 1 is 8.68 square inches.

The area of Triangle 1 is 6.48 square inches.

The area of Rectangle 2 is ... square inches.

The area of Triangle 2 is ...  square inches.

The area of the whole figure is ... square inches.

Answer 1

From the figure,

AE = 2.4

EB = 2.8

BC = 11.7

Area of rectangle 1 = 8.68 sq.in

`\Rightarrow FH * HI=8.68`

`\Rightarrow EB * HI=8.68` (∵ sides of the rectangle 2)

`\Rightarrow 2.8 * HI=8.68`

`\Rightarrow HI=3.1`

Area of Triangle 1 = 6.48 sq.in

`\Rightarrow (1)/(2)* AE * EG= 6.48`

`\Rightarrow (1)/(2)* AE * (EF+FG)= 6.48`

`\Rightarrow (1)/(2)* AE * (EF+HI)= 6.48` (∵ sides of the rectangle 1)

`\Rightarrow EF+3.1= 5.4`

`\Rightarrow EF=2.3`

`\Rightarrow BH=2.3` (∵ sides of the rectangle 2)

`BC = BH+HI+IC`

`\Rightarrow 11.7= 2.3+3.1+IC`

`\Rightarrow IC=6.3`

The area of Rectangle 2,

`=EB* BH =2.8* 2.3=6.44\ sq.in`

The area of Triangle 2,

`(1)/(2)* GI * IC=(1)/(2)* EB * IC=(1)/(2)* 2.8 * 6.3=8.82\ sq.in`

The area of the whole figure = Area of Triangle 1 + Area of rectangle 1 + Area of Triangle 2 + Area of rectangle 2

= 6.48+8.68+8.82+6.44=30.42 sq.in