Page 275 - Start Up Mathematics_8 (Non CCE)

Example 16: Find the area of a trapezium whose parallel sides are 36 cm and 12 cm and the non-parallel
sides are 15 cm each.
W 12 cm R
Solution: Let WRAP be the given trapezium.
WR = 12 cm, PA = 36 cm

WP = RA = 15 cm
15 cm h h 15 cm
Let WT be h cm and PT be x cm.
\ SA = 24 – x cm 24 – x
x 12 cm
In D WTP, P T 36 cm S A

2
2
WT = WP – PT 2
2
2
2
2
fi h = (15) – (x) = 225 – x (1)
In D RAS,
2
2
RS = RA – SA 2
2
2
2
fi h = (15) – (24 – x) = 225 – 576 + 48x – x 2
2
= – 351 + 48x – x (2)
From equation (1) and (2), we get,
2
225 – x = –351 + 48x – x 2
2
2
fi 225 + 351 = x – x + 48x Puzzle
fi 576 = 48x I have a 2 × 8 chocolate bar. If I can
break this either along its length or
576 its breadth, then how many times
fi = x
48 do I need to break the bar in order
fi x = 12 cm to obtain 1 × 1 pieces?
Now putting x in equation (1), we get
2
2
2
fi h = (15) – (12) = 225 – 144 = 81
fi h = 9 cm
1 1
\ Area of trapezium WRAP = × 9 × (36 + 12) = × 9 × 48 = 216 cm 2
2 2
2
Hence, the area of trapezium WRAP = 216 cm .

EXERCISE 17.2

1. Find the area of the trapezium whose:
(a) bases = 15 cm and 20 cm and altitude = 8 cm
(b) bases = 10 cm and 12 cm and altitude = 5 cm
2. Find the area of a trapezium whose parallel sides are 77 cm and 60 cm and the other sides are 25 cm
and 26 cm.
2
3. The area of a trapezium is 105 cm . If one of the parallel sides is 28 cm and the distance between
the parallel sides is 5 cm, find the length of the other parallel side.
4. Find the area of the trapezium PART whose sides PA = 10 cm, PT = AR = 10 cm and
TR = 22 cm. Also PA || TR.
5. Top surface of a table is trapezium in shape. Find its area if its parallel sides are 1.5 m and 2 m and
the perpendicular distance between them is 1.2 m.

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