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Alona [7]
3 years ago
6

Lori creates the following design for a T-shirt.

Mathematics
1 answer:
kakasveta [241]3 years ago
6 0

<u>Solution-</u>

From the figure,

AE = 2.4

EB = 2.8

BC = 11.7


Area of rectangle 1 = 8.68 sq.in

\Rightarrow FH \times HI=8.68

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

\Rightarrow 2.8 \times HI=8.68

\Rightarrow HI=3.1


Area of Triangle 1 = 6.48 sq.in

\Rightarrow \frac{1}{2}\times AE \times EG= 6.48

\Rightarrow \frac{1}{2}\times AE \times (EF+FG)= 6.48

\Rightarrow \frac{1}{2}\times AE \times (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\times BH =2.8\times 2.3=6.44\ sq.in


The area of Triangle 2,

\frac{1}{2}\times GI \times IC=\frac{1}{2}\times EB \times IC=\frac{1}{2}\times 2.8 \times 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


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