Question

What are the areas of each one?

Answer 1

Answer:

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1. 62
2. 7

Step-by-step explanation:

1. Two squares of equal area and a triangle

Area of one square = S²

Area = 5²

Area = 25

Area of the two suares = 25 x 2

Area=50

Area of triangle;

Using heron's formula, $A=\sqrt{s(s-a)(s-b)(s-c)}$

a= 5, b=5, c=6

s= (a+b+c)/2

s=(5+5+6)/2

s=16/2

s=8

$A=\sqrt{8(8-5)(8-5)(8-6)}$

$A=\sqrt{8(3)(3)(2)}$

$A=\sqrt{144}$

A=12

total area = area of two squares + area of triangle

total area=50+12

total area = 62

2. in this drawing there are two big equal squares merging and forming a smaller square in between.

Area of each big square = 2 x 2

Area =4

the small square is formed at the midpoint of the sides of the bigger squares

it's sides will be half of the bigger squares

it's area = 1 x 1

Area = 1

to get the area of the entire shape, we need to get the area of the big square excluding the small square formed inside each of them

∴ area of big square without small square = area of big square - area of small square

Area = 4-1

Area = 3

Are of total shape = area of small square + (2 x area of big square without small square)

(note: the 2 x is because the are two big squares)

Area = 1 +(2 x 3)

Area = 1 + 6

Area = 7