Question

A square has a diagonal length of 5 cm what is the area of a square

Answer 1

Area of square = 12.48 cm^2

Explanation:

Since the square has all sides equal, and when diagonal is made, square form two right angled triangles. Using Pythagoras theorem we can find the length of side of the square.

`c^2 = a^2 + b^2`

where c = 5cm and a==b (square has all sides equal)

Putting value of b = a

`(5)^2 = a^2 + a^2\\25 = 2 a^2\\25/2 = a^2\\=> a^2 = 12.5\\ => √(a^2) = √(12.5)\\=> a = 3.53\, cm`

So, length of side of square = 3.53

Area of square = (3.53)^2

Area of square = 12.48 cm^2.

Answer 2

Hello!

The answer is:

The area of the given square is equal to
`12.5cm^(2)`

`Area=12.5cm^(2)`

Why?

To solve the problem, we don't need to calculate the length of the sides of the square. We are given the diagonal length of the square, so using the following formula, we can calculate the are of the square without knowing the sides:

`Area=(diagonal^(2) )/(2)`

So, substituting we have:

`Area=((5cm)^(2) )/(2)=(25cm^(2) )/(2)=12.5cm^(2)`

Hence, we have that the area of the given square is equal to
`12.5cm^(2)`

Have a nice day!