# IDENTIFY TRAPEZIUMS

## About "Identify trapeziums"

Identify trapeziums :

What is trapezium ?

A quadrilateral in which one pair of opposite sides is parallel called trapezium.

Various types of trapeziums are,

• right trapezoid
• An acute trapezoid
• obtuse trapezoid
• isosceles trapezoid
• parallelogram

Right trapezoid :

A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. Right trapezoids are used in the trapezoidal rule for estimating areas under a curve. Acute trapezoid :

An acute trapezoid has two adjacent acute angles on its longer base edge Obtuse trapezoid :

An obtuse trapezoid has one acute and one obtuse angle on each base. Isosceles trapezoid :

An isosceles trapezoid is a trapezoid where the sides (legs) have the same length, and the base angles have the same measure. It has reflection symmetry. This is possible for acute or right trapezoids. Parallelogram :

A parallelogram is a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse or right trapezoids.

A tangential trapezoid is a trapezoid that has an incircle. ## Area of trapezium

Area = (1/2) (a + b) x h

Example 1 :

In a trapezium the measurement of one parallel side two more than the other parallel side and the height is 4 cm. The area of the trapezium is 64 cm². Find the two parallel sides.

Solution :

Area of the trapezium = 64 cm²

Let  "a" and "b" are two parallel sides

One parallel side is two more than the other parallel side. So we can assume b as a + 2

Area of a trapezium = (1/2) (a + b) x h

(1/2) (a + b) x h  =  64

(1/2) (a + a + 2) x 4 = 64

(1/2) (2a + 2) x 4 = 64

2 (2a + 2) = 64 ==>  2a + 2 = 32

2a = 30 ==> a = 15 cm

b = a + 2 ==> b = 15 + 2 ==> b = 17 cm

Therefore the two parallel sides are 15 cm and 17 cm.

Example 2 :

The height of a trapezoid is 8 in. and its area is 96 square inches. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?

Solution :

here, h = 8 inches

Area of the trapezoid = 96 square inches

base lengths are b₁ and b₂ respectively.

b₁ = b₂ + 6

(1/2) x 8 (b₂ + 6 + b₂) = 96

4 (2b₂ + 6) = 96

2b₂ + 6 = 24

2b₂ = 18

b₂ = 9

By applying the value of b₂ in the equation b₁ = b₂ + 6, we get

b₁ = 9 + 6  ==> b₁ = 15 inches

Hence, base lengths are 9 inches and 15 inches After having gone through the stuff given above, we hope that the students would have understood "Identify trapeziums".

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