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Find the area:1. Base = 10 cm, height = 2 cm 10cm2 2. Base = 6 m, height = 4 m 12m2

Find the base of the triangle:3. area = 96 cm2, height = 16 cm 24cm

Warm Up

Find the height of the triangle:4. Base = 11ft, area = 11 ft2 2ft

5. Base = 12 in, area = 48 in2 8in.

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What is a triangle?

A triangle is a kind of polygon that has three sides.

Examples of triangles:

Let’s review what we have Let’s review what we have learnt in the last lessonlearnt in the last lesson

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Area of a Triangle

The area of a triangle is given by "half of base times height“.

Area =

where

b  is the length of the baseh  is the height of the triangle.

Note: The height is the length of a line

segment perpendicular to the base of the triangle.

12

x b x h

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• A quadrilateral in which one pair of opposite sides are parallel

• ABCD is a trapezoid in which AB || DC, but AD is not parallel to BC.

BA

CD

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•A trapezoid is called an isosceles trapezoid, when its non parallel sides are equal.

• A trapezoid is called a right trapezoid, when it has at least two right angles.

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• The two parallel sides of a trapezoid are called its bases. In the trapezoid ABCD, AB and DC are bases.

• The two sides that are not bases are called legs of a trapezoid. AD & BC are the legs of the trapezoid ABCD.

Bases, legs and height of a trapezoidBases, legs and height of a trapezoid

BA

CD

E

F

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•A height of a trapezoid is a line segment that is perpendicular to the bases of the trapezoid. DE = BF is the height of the trapezoid ABCD

• The median of a trapezoid is the line segment whose endpoints are the midpoints of the legs of the trapezoid. GH is the median of the trapezoid ABCD.

BA

CD

E

F

G H

Bases, legs and height of a trapezoidBases, legs and height of a trapezoid

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Area of a Area of a trapezoidtrapezoid

To find the area of a trapezoid, consider the following trapezoid ABCD.

BA

CD

E

F

Here, DB is the diagonal which divides the trapezoid into two triangles. Now,

Area of trapezoid ABCD = Area of triangle ABD + Area of triangle DBC

= 1/2 * AB * DE + 1/2 * DC * BF

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But, DE = BF which is nothing but the altitude or height ‘ h’

Let, AB = b1 and DC = b2 be the two parallel sides of the trapezoid

Therefore,

Area of trapezoid, A = 1/2 * h (b1 + b2)

BA

CD

E

F

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Area of Area of trapezoidstrapezoids

The area of trapezoid is equal to half the product of sum of the parallel sides and the perpendicular distance between them.

Area of trapezoid, A = 1/2 * h (b1 + b2)

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Example 1:

The parallel sides of a trapezoid are 32 cm and 44 cm. If the

altitude is 12 cm, find its area.

b1 = 32 cm, b2 = 44 cm, h = 12 cm , A = ?

Area of the trapezoid, A = 1/2 * h (b1+b2)

= 1/2 * 12 (32+44)

= 456 cm²

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Example 2:

The area of a trapezoid is 130 cm²and its bases are 26 cm and 39 cm. Find the height of the trapezoid.

b1 = 26 cm, b2 = 39 cm, A = 130 cm² and h = ?

Area of the trapezoid, A = 1/2 * h (b1+b2)

Height of the trapezoid, h = 2A / (b1+b2)

= (2 * 130) / (26+39)

= 4 cm

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Example 3:

The area of a trapezoid of altitude 8 cm is 320 cm².If

one of the parallel sides is 25 cm, find the length of the

other side.

b1 = 25 cm, h = 8 cm, A = 320 cm² and b2 = ?

Area of the trapezoid, A = 1/2 * h (b1+b2)

Length of the base, b2 = (2A /h) – b1

= (2 * 320/8) - 25

= 55 cm

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1. The parallel sides of a trapezoid are 24 cm & 36 cm and the altitude is 11 cm. Find its area

Answer: 330 cm²

2. The area of a trapezoid is 360 m². The two parallel sides are 28 m and 12 m. Find the perpendicular distance between the parallel sides.Answer: 18 m

3. Find the sum of the lengths of parallel sides of a trapezoid whose area is 0.54 m² and altitude is 9 cm.Answer: 12 m

4. The area of a trapezoid of altitude 6 cm is 240 cm². If one of the parallel sides is 45 cm, find the length of the other side.Answer: 35 cm

Your Turn

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5. The two parallel sides of a trapezoid are 300 cm & 4.5 m. If its area is 2500 cm², find the perpendicular distance between the parallel sides. Answer: 6.67 cm

6. Two parallel sides of a trapezoid are in the ratio 2:5. The perpendicular distance between them is 9 cm. If the area of the trapezium is 315 cm², find the sides. Answer: 20 cm, 50 cm

7. The sum of the parallel sides of a trapezoid is 0.9 m. If the area of trapezoid is 360 cm², find the perpendicular distance between the parallel sides. Answer: 8 cm

Your Turn

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8. The area of a trapezoid is 210 cm²and its height is 14 cm. If one of the bases is longer than the other by6 cm, find its bases.

Answer: 12 cm, 18 cm

9. The area of trapezoid is 180 cm²and its height 0.12 m. If one of the parallel sides is half of the other, find the lengths of the two parallel sides.Answer: 10 cm, 20 cm

10. The difference of the parallel sides of a trapezoid is 25 cm. If the area of the trapezoid is 240 m²and the altitude is 12 m , find the lengths of its bases.Answer: 7.5 cm, 32.5 cm

Your Turn

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Refreshment time

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1. One of the parallel sides of an isosceles trapezoid is longer than the other by 4 cm. The perimeter of the trapezoid is 40 cm and the lengthof the legs is 8 cm. If the perpendicular distance between the parallel sides is 6 cm, find the area of the trapezoid and lengths of all the sides.

h = 6 cm, perimeter = 40 cmLet b1 = x cmSo, b2 = X+4 cmLet b3 & b4 be the legs of the trapezoid.As the trapezoid is isosceles, b3 = b4 = 8 cmThe perimeter of the trapezoid = b1+b2+b3+b4 40 = x+(x+4)+8+8 x = 10 cmTherefore, the lengths of the parallel sides, b1 = 10 cm & b2 =14 cmThe area of the trapezoid, A = 1/2 h(b1+b2) ; = 1/2 * 6(10+14)

= 72 cm²

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2. If the area of the following trapezium is 127 cm², find the lengths of the parallel sides.

3x + 4

4 cm

2x-1

b1 = 2x –1 , b2 = 3x+4, h = 4 cm , Area, A = 127 cm², x = ?

The area of the trapezoid = 1/2 h (b1+b2)

127 = 1/2 * 4 [(2x-1)+(3x+4)]

x = 12.4 cm

So, the lengths of the parallel sides, b1 = 23.8 cm, b2 =41.2 cm

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3. The trapezoid shaped farm has parallel sides of length 150 m and 250 m. The perpendicular distance between the parallel sides is35 m. Find the cost of giving manure to the farm at 3.5 $/quintal if, 250 kg of manure have to be fed per hectare.

b1 = 150 m, b2 = 250m, h = 35 m, Area, A = ?

The area of the trapezoid shaped farm, A = 1/2 h(b1+b2)

A = 1/2 (35)(150+250)

A = 7000 m²

1 hectare = 10000 m²

For 10000 m², the quantity of manure required = 250 kg

For 7000 m², the quantity of manure required = (250/10000)* 7000

= 135 kg

The cost of giving 135 kg of manure to the farm = (3.5/100)* 135

= $ 4.72

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1. Trapezoid is a quadrilateral in which one pair of opposite sides are parallel.

2. When the non parallel sides of a trapezoid are equal, the trapezoid is called an isosceles trapezoid.

3. A right trapezoid is one which has at least two right angles

4. The two parallel sides of a trapezoid are its bases, the two non parallel sides are its legs.

Let’s summarize what we have learnt today

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5. A line segment that is perpendicular to the bases of the trapezoid is the height of the trapezoid

6. A line segment whose endpoints are the midpoints of the legs of the trapezoid is the median of the trapezoid.

7. The area of the trapezoid is equal to half the product of its altitude and the sum of its parallel

sides.i.e A = 1/2 * h (b1+b2)

Let’s summarize what we have learnt today

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