# Area of Trapezoid

In this section we will discuss area of trapezoid.Trapezoid is a quadrilateral whose two sides are parallel to each other. In

**trapezium (trapezoid)**ABCD such that AB and CD area parallel sides where AD and BC are its non-parallel sides.

Here, the length of parallel sides are a and b and the distance between them is h.

**•**Area of trapezium = 1/2 ( sum of two bases ) x height

**•**Area = 1/2 x (a + b) x h.

**•**Median of trapezoid = ( a + b) / 2

**Base :**Each of the two parallel sides of a trapezoid is called a base of trapezoid.

**Altitude or height :**The distance between the two parallel sides is called the height or altitude of the trapezoid.

**Median of trapezoid :**Its length equals the arithmetic mean of the lengths of the bases.

**Some solved examples**

1) Find the area of trapezoid whose parallel sides are of lengths 10 cm and 12 cm and the distance between them is 4 cm.

**Solution :**

Two parallel sides, a = 10 cm and b = 12 cm; height =h = 4 cm.

Area = ½ x ( a + b) x h

Area = ½ x ( 10 + 12 ) x 4

Area = ½ x 22 x 4

Area = 44 cm

^{2}

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2) Find the sum of the lengths of the bases of a trapezoid whose height is 11 cm and area is 0.55 m

^{2}.

**Solution :**

Height = h = 11 cm = 11 / 100 = 0.11 m; Area = 0.55 m

^{2}

Area = ½ x (a +b) x h

0.55 = ½ x (a + b) x 0.11

(a + b) =( 0.55 x 2) / 0.11

( a + b) = 10 cm

∴ Sum of parallel sides = 10 cm.

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3) Find the area of the following figure.

**Solution :**

Area of trapezium = ½ x (a + b) x h

= ½ x ( 18 + 7) x 8

Area of trapezium = 100 cm

^{2}

Area of square = side x side

= 18 x 18

Area of square = 324 cm

^{2}

∴ Area of (ABCDEF ) = Area of trapezium + Area of square

⇒ = 100 + 324

Area of (ABCDEF ) = 424 cm

^{2}

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4) Find the median of the following trapezoid.

**Solution :**

Median of trapezoid = ( a + b) / 2

= ( 6 + 8) / 2

∴ Median of trapezoid = 7 cm.

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**Mensuration : Area and Perimeter**

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

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