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

a = ½bh
a = ½ x 5 x 8 = \( \frac{40}{2} \) = 20

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

a² - 4a - 12 = 0
(a + 2)(a - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 2) or (a - 6) must equal zero:

If (a + 2) = 0, a must equal -2
If (a - 6) = 0, a must equal 6

So the solution is that a = -2 or 6

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\( \sqrt{2} \)

When solving an equation with two variables, 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.)

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).