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

sa = 2πr² + 2πrh
sa = 2π(8²) + 2π(8 x 4)
sa = 2π(64) + 2π(32)
sa = (2 x 64)π + (2 x 32)π
sa = 128π + 64π
sa = 192π

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 7 x 7 = \( \frac{49}{2} \) = 24\(\frac{1}{2}\)

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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 8 + 7 + 6 + 2
p = 23