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(3 + 4)(3)
a = ½(7)(3)
a = ½(21) = \( \frac{21}{2} \)
a = 10\(\frac{1}{2}\)

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 < sign and the answer on the other.

-2c + 1 < \( \frac{c}{1} \)
1 x (-2c + 1) < c
(1 x -2c) + (1 x 1) < c
-2c + 1 < c
-2c + 1 - c < 0
-2c - c < -1
-3c < -1
c < \( \frac{-1}{-3} \)
c < \(\frac{1}{3}\)

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

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 3)
sa = 2π(1) + 2π(3)
sa = (2 x 1)π + (2 x 3)π
sa = 2π + 6π
sa = 8π

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 d° = 147, the value of a° is 33.

A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.