To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 1² + 1²
c² = 2
c = \( \sqrt{2} \)

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(3²) + 2π(3 x 5)
sa = 2π(9) + 2π(15)
sa = (2 x 9)π + (2 x 15)π
sa = 18π + 30π
sa = 48π

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 5 x 7) + (2 x 7 x 9) + (2 x 5 x 9)
sa = (70) + (126) + (90)
sa = 286

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 5cm + 10cm + 5cm = 20cm

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.