Question

What is the area of the shaded square? A 7 cm² C 49 cm² B 25 cm² D 60 cm² 3 cm 4 cm

Answer 1

The area of a square is given by the square of one of its sides. To find the area of the shaded square first we need to find the length of its side.

The side of the shaded square along the sides of the other squares form a right triangle, where the side of the shaded square is the hypotenuse.

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the legs. If we call the side of the shaded square as x, using the Pythagorean Theorem we have the following equation

`3^2+4^2=x^2`

Solving for x, we have

`\begin{gathered} 3^2+4^2=x^2 \\ 9+16=x^2 \\ x=\sqrt[]{25} \\ x=5 \end{gathered}`

Then, the area of the shaded square is

`5^2=25`

The area of the square is 25cm².