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 squ…

Question

asked Sep 20, 2019 101k views

1 Answer

Ssinfod · Answer 1 · 2019-09-26T13:03:40+0000

Solution-

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