The diagram shows a right-angled triangle.
Squares are drawn on each of the three sides.

Square R
Square PS
Square Q

Area of Square P= 17 cm”.
Area of Square R = 50 cm?
Work out the area of Square Q.

Area of a square is defined as

Area = (side)^2

Let's start with square p. Square p has area = 17cm^2

Plug 17cm^2 into our area formula

17cm^2 = (side)^2. Take the square root of each side.

Sqrt(17) cm = side.

Every side for square p = sqrt(17) cm.

Next, square R has an area of 50 cm^2. Plug that into our formula.

50 cm^2 = (side)^2. Take the square root of each side.

Sqrt(50) = side.

Every side for square R = sqrt(50)

We now have one leg and the hypotenuse of a right triangle. Plug this into the pythagorean theorem.

b is the length of a side for square Q

(Sqrt(17))^2 + b^2 = (sqrt(50))^2. Square every term.

17 + b^2 = 50. Subtract 17 from both sides.

b^2 = 33. Take the square root of each side.

b = sqrt(33)

Each side of square Q = sqrt(33).

Plug sqrt(33) into our area formula.

A = (sqrt(33))^2. Solve for A

A = 33.

The area of square Q = 33 square centimeters.