Posted by **Michele** on Wednesday, February 23, 2011 at 5:50pm.

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 -
**Helper**, Wednesday, February 23, 2011 at 7:15pm
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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