# geometry

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If the area of a square is 100 cm. What is the area of each triangle produced if you draw two diagonals in the square?

• geometry -

Area of square = side s^2
100 = s^2
s = 10

The diagonals of a square bisect each other and meet at 90 degrees.

The diagonals of a square bisect its angles.

The diagonals of a square are perpendicular.

The diagonals of a square are equal.

This means that the two diagonals create 4 triangles of equal area.

To find the length of the equal diagonals d,

d = s * (sqrt(2))
s = 10
d = 10(sqrt(2))
d/2 = 10(sqrt(2))/2 = 5(sqrt(2))

Since, the diagonals of a square bisect each other and meet at 90 degrees, the four triangles are each 45-45-90 degrees.

side = hypotenuse = 10
leg = 1/2 d = 5(sqrt(2))
leg = 1/2 d = 5(sqrt(2))

One leg = height
One leg = base
Area = 1/2 bh
A = 1/2 5(sqrt(2)) * 5(sqrt(2))
A = 1/2 * 50
A = 25 cm^2

Each triangle's area is,
25 cm^2

Draw a picture so you can follow the above.

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