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\( \sqrt{2} \)

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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.

(4a)(8ab) - (7a²)(6b)
(4 x 8)(a x a x b) - (7 x 6)(a² x b)
(32)(a¹⁺¹ x b) - (42)(a²b)
32a²b - 42a²b
-10a²b

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

-6c(c - y)
-6(2)(2 + 5)
-6(2)(7)
(-12)(7)
-84