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Trapezoid

A trapezoid is a quadrilateral with one pair of parallel lines

Bases - The two parallel lines are called the bases.

The Legs - The two non parallel lines are the legs.

Diagram 1
Diagram 2

Properties

• Property #1) The angles on the same side of a leg are called adjacent angles and are supplementary( more )
• Property #2) Area of a Trapezoid = $$Area = height \cdot \left( \frac{ \text{sum bases} }{ 2 } \right)$$ ( more )
• Property #3) Trapezoids have a midsegment which connects the mipoints of the legs( more )

The angles on the same side of a leg are called adjacent angles such as $$\angle A$$ and $$\angle D$$ are supplementary. For the same reason, $$\angle B$$ and $$\angle C$$ are supplementary.

Practice Problems

Problem 1

$$\angle ZWX = 180 − 44 = 136°$$

Problem 2

$$\angle MLO = 180-124 = 56°$$

Problem 4

If LMNO is a trapezoid and its bases LO and MN are parallel then, $$\angle MNO$$ and $$\angle NOL$$ which must be supplementary however, the sum of these angles is not 180 111 + 68 ≠ 180.

Area of Trapezoid

Problem 5

$Area = height \cdot \left( \frac{ \text{sum bases} }{ 2 } \right) \\ = 7 \cdot \left( \frac{ 4 + 8 }{ 2 } \right) \\ =7 \cdot \left( \frac{ 12 }{ 2 } \right) \\ = 7 \cdot 6 \\ = \fbox {42 } ft^2$

Midsegment of Trapezoid

Problem 6

To calculate the length of the midsegment find the average of the bases length of midsegment = (6 + 4) / 2 = 5.

Midsegment of Trapezoid

The midpoint of the red segment pictured below is the point $$(A, 2b)$$ (click button below to see).

The midsegment of a trapezoid is the segment that joins the midpoints of the nonparallel sides of a trapezoid.

In the trapezoid below, the midpoints of the non-parallel sides are points S and V. The midsegment is the red line segment from S to V.

Example Midsegment
Trapezoid #10
Step 1
Calculating the length of the bases . Upper Base:
$$35 - 16 = 9$$
Step 2
Calculating Low Base:
$$45 - 0 = 45$$
Step 3
Calculating the sum of the bases
$$9 + 45 = 54$$
Step 4
Divide the sum by 2
$$\frac {54}{2} = \boxed{27}$$
Problem 8
Step 1
Calculating the length of the bases . Upper Base:
$$17 - 8 = 9$$
Step 2
Calculating Low Base:
$$20 - 0 = 20$$
Step 3
Calculating the sum of the bases
$$9 + 20 = 29$$
Step 4
Divide the sum by 2
$$\frac {29}{2} = \boxed{14.5}$$
Problem 9

It is not a true midsegment because its length does not equal half the sum of the lengths of the bases.