A trapezoid is a flat geometric shape with four straight sides having at least one pair of opposite parallel sides. It looks like a triangle whose top portion is sliced off.

The parallel sides are the bases, and the other two sides are called the legs or the lateral sides. It is also called a trapezium in the UK and some other parts of the world.

Properties

Has four sides and four angles; in trapezoid ABCD, AB, BC, CD, and DA are the four sides making angles ∠DAB, ∠ABC, ∠BCD, and ∠CDA

Has one pair of parallel sides. The two parallel sides are the bases while the non-parallel sides are the legs; here, AD = short base, BC = long base, while AB = Leg 1 and CD = Leg 2, and AD ∥ BC

The adjacent angles add up to180°; so, ∠DAB +∠ABC = 180°, ∠ABC + ∠BCD = 180°, ∠BCD + ∠CDA = 180°, and ∠CDA + ∠DAB = 180°

The median is parallel to the two bases and divides the non-parallel sides into two equal parts; so, EF ∥ AD and EF ∥ BC

Formulas

Median

It is the line segment mid-way between the two bases. It is also called a midline or a mid-segment. The formula is given below:

Find the median of a trapezium with bases measuring 7 m and 9 m.

Solution:

As we know, Median (M) = ½ (a + b), here a = 9 m and b = 7 m = ½ (9 + 7) m = 16/2 m = 8 m

Area

The total space enclosed by the trapezoid. The formula is given below:

Find the area of a trapezoid when two bases are 8 cm and 6 cm, and the height is 10 cm

Solution:

As we know, Area (A) = ½ (a + b) × h, here a = 8 cm, b = 6 cm, and h = 10 cm =1/2 × (8 + 6) × 10 cm^{2} = ½ × 14 × 10 cm^{2} = 70 cm^{2}

Problem: Finding the area of a trapezoid when the MEDIAN and HEIGHT are known

Find the area of a trapezoid which has a median 5 cm and height is 11 cm

Solution:

Here we will use an alternative formula, A = m × h, here m = median and h = height In this trapezoid, m = 5 cm and h = 11 cm Since, A = m × h = 5 × 11 cm^{2} = 55 cm^{2}

Perimeter

The total distance covered around the edge of the trapezoid. The formula is given below:

Find the perimeter of a trapezoid with sides measuring 6 m, 8 m, 12 m, and 15 m.

Solution:

As we know, Perimeter (P) = a + b + c +d, here a = 15 m, b = 12 m, c = 6 m, and d = 8 m = 15 m + 12 m + 6 m + 8 m = 41 m

Types

Trapezoids are classified into two groups: based on sides, 1) scalene and 2) isosceles trapezoid; based on angles, 1) acute, and 2) obtuse, and 3) right trapezoid.

The differences between the types are given below: