Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 1 + 6 + 2 + 8
p = 17

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

2c - 7 = \( \frac{c}{-3} \)
-3 x (2c - 7) = c
(-3 x 2c) + (-3 x -7) = c
-6c + 21 = c
-6c + 21 - c = 0
-6c - c = -21
-7c = -21
c = \( \frac{-21}{-7} \)
c = 3

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(5a)(9ab) + (5a²)(6b)
(5 x 9)(a x a x b) + (5 x 6)(a² x b)
(45)(a¹⁺¹ x b) + (30)(a²b)
45a²b + 30a²b
75a²b