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

a = ½bh
a = ½ x 1 x 7 = \( \frac{7}{2} \) = 3\(\frac{1}{2}\)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 14cm + 13cm + 14cm = 41cm

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 + 9)(4)
a = ½(17)(4)
a = ½(68) = \( \frac{68}{2} \)
a = 34

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 c° = 22, the value of y° is 158.