The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(8 + 5)(3)
a = ½(13)(3)
a = ½(39) = \( \frac{39}{2} \)
a = 19\(\frac{1}{2}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

6a⁸ - 5a⁸ = 1a⁸

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with z° = 37, the value of a° is 37.

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 3² + 6²
c² = 9 + 36
c² = 45
c = \( \sqrt{45} \)

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 5 x 2
a = 10