A trapezoid is a quadrilateral with one pair of parallel sides, called the bases. Trapezoids appear in bridge supports, roof shapes, ramps, and many geometric designs because their slanted sides can connect different widths. Understanding their properties helps you find missing lengths, angles, midsegments, and areas.
The key idea is that the two bases stay the same distance apart when measured perpendicularly.
Key Facts
- A trapezoid has one pair of parallel sides called bases, usually labeled b1 and b2.
- The height h is the perpendicular distance between the two bases, not the length of a slanted side.
- Area of a trapezoid: A = 1/2(b1 + b2)h.
- The midsegment connects the midpoints of the legs and is parallel to both bases.
- Midsegment length: m = 1/2(b1 + b2).
- In an isosceles trapezoid, the legs are congruent, each pair of base angles is congruent, and the diagonals are congruent.
Vocabulary
- Trapezoid
- A quadrilateral with one pair of parallel sides.
- Base
- One of the parallel sides of a trapezoid.
- Leg
- One of the nonparallel sides of a trapezoid.
- Height
- The perpendicular distance between the two bases of a trapezoid.
- Midsegment
- The segment joining the midpoints of the legs of a trapezoid.
Common Mistakes to Avoid
- Using a slanted leg as the height is wrong because height must be perpendicular to the bases.
- Forgetting to add the bases before dividing by 2 in A = 1/2(b1 + b2)h gives an area that is too small or based on only one base.
- Assuming every trapezoid is isosceles is wrong because equal legs, equal base angles, and congruent diagonals happen only in isosceles trapezoids.
- Confusing the midsegment with a diagonal is wrong because the midsegment connects the midpoints of the legs and runs parallel to the bases.
Practice Questions
- 1 A trapezoid has bases b1 = 8 cm and b2 = 14 cm, and height h = 6 cm. Find its area.
- 2 The midsegment of a trapezoid is 18 in and one base is 12 in. Find the length of the other base.
- 3 A trapezoid has congruent legs and one bottom base angle of 70 degrees. Explain what type of trapezoid it is and find the other bottom base angle.