Question

If the diagnol of a square is 50 cm. find its area
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Answer 1

Answer:

All the four sides of a square are equal in length and are perpendicular to each other i.e, form 90 degree angle with each other. As you can see in the diagram, “Angle1” is 90 degree.

If we consider ABD as a triangle, then since sides AB and AD are equal, Angle2 and Angle3 are equal to each other because of the property : “Angles opposite to equal sides in a triangle are equal”.

We have Angle1 = 90, Angle2 == Angle3

Using the property: “Sum of all three angles of triangle = 180”.

90 + Angle2 + Angle3 = 180

Angle2 + Angle3 = 180 - 90

Angle2 + Angle3 = 90

2 * Angle2 = 90 (since Angle2 == Angle3)

Angle2 = 45

Therefore Angle2 == Angle3 == 45

Now, We have Angle1 = 90, Angle2 =45, Angle3 = 45

Using trigonometric ratio Sin(X) = Perpendicular/Hypotenuse

-> Sin(Angle2) = AD/DB

-> Sin(45) = AD/50

-> AD = 50/root(2)

Therefore, AD == AB == 50/root(2)

Area of Square = AB * AD

-> (50/root(2)) * (50/root(2))

->2500/2

-> 1250 units.