# Mensuration Part 1

1. The parallel sides of trapezium are 11cm and 9cm long and the distance between them is 6cm.Find its area?

A.26cm^{2}

B.60Cm^{2}

C.40cm2

D.45CM^{2}

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Ans: (B)

Sol. Area of the trapezium =1/2(sum of the parallel side)

=1/2(11+9) X 6

=1/2 X 20 X 6=60cm^{2}

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2. Area of a trapezium is 360cm^{2}. Length of one of the parallel sides is 16cm and the distance between them is 8cm. find the length of the other parallel side?

A.64cm

B.74cm

C.56cm

D.36cm

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Ans: (B)

Sol. One of the parallel sides=16cm

The “l” of the other parallel side is x cm

Area of the trapezium=360cm^{2}

D=8cm

x=1/2(a+b) h

x=1/2(16+x)8

360=128+8x/2

360=64+4x

360-64=4x

296=4x

x=74cm

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3. The radius of a circle is 21cm. Find its area?

A.1452cm^{2}

B.1386cm^{2}

C.1561cm^{2}

D.1981cm^{2}

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Ans: (B)

Sol. R=21cm

A=π r^{2}

=22/7 x 21 x 21=1386cm^{2}

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4. The ratio of the lengths of the parallel sides of a trapezium is 2:1. The distance between them is 16cm. if the area of the trapezium is 270cm^{2}, find the lengths of the parallel sides?

A.30,60cm

B.40,60cm

C.30,40cm

D.40,50cm

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Ans: (A)

Sol. Area of the trapezium=270cm^{2}

D between the parallel sides=6cm^{2}

Let the length of the parallel sides be 2x and x cm

Area= 1/2(a+b) h

270=1/2(2x+x) x 6

270=18x/2

x=270 x 2/18=30cm

Length of the parallel sides= 2x and x

x=30cm

2x=2 x 30=60cm

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5. Find the area of the rhombus whose diagonals are of length 2.8 and 6.5cm?

A.6.5cm^{2}

B.7.5cm^{2}

C.9.1cm^{2}

D.8.4cm^{2}

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Ans: (B)

Sol. Area of the rhombus= 1/2 d_{1 }d_{2}

d_{1}=2.8cm d_{2}=6.5cm

Area=1/2 x 2.8 x 6.5=9.1cm^{2}

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6. A wire is bent into the form of a square of the side 11cm.The wire is straightened and bent into the form of a circle. What will be the radius of the circle so formed?

A.5cm

B.6cm

C.9cm

D.7cm

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Ans: (D)

Sol. Side of square=11cm

Perimeter of square=4 x s

=4 x 11=44cm

When the same wire is straightened and bent into the form of a circle, then it represents the circumference of the circle=44cm

Let “r” be the radius

Then circumference=2 pie r

2 x 22/7 x r cm=44cm

r=44 x 7/22 x 2=7cm

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7. The area of the circle is 154cm. Find its radius?

A.6cm

B.7cm

C.8cm

D.9cm

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Ans: (B)

Sol. Area given=154cm^{2}

Area= ᴨ r^{2}

154=22/7 r^{2}

r^{2}=154 x 7/22=49

r^{2}=49cm

r=7cm\

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8. The area of a rhombus is 360cm^{2} and one of the diagnols is 15cm^{2}. Find the other diagnol?

A. 38cm

B.48cm

C.58cm

D.68cm

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Ans: (B)

Sol. Length of the diagnol(d_{1})=15cm

Length of the other=d_{2}

Area of the rhombus =1/2 d_{1 }d_{2}=360cm^{2}

So, 360 cm^{2} =1/2 x 15 x d_{2}

360cm^{2}=15/2d_{2}

360 x 2/15=48cm

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9. The base area of a cuboid is 36cm^{2 }and its volume is 432cm^{2}. Find the height?

A.9cm

B.8cm

C.10cm

D.12cm

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Ans: (D)

Sol. V=432cm^{2}, base area=36cm^{2}

Volume of a cuboid =Base x Height

Hence height=Volume/Base area

432/36=12cm

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10. Find the perimeter of a rectangle whose area is 496 sq.mts and breath is 8mts?

A.140mts

B.160mts

C.218mts

D.188mts

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Ans: (A)

A. Area of a rectangle=L x B

Breath=8mts

Area given =496

L=496/8=67mts

P of the rectangle=2(L+B)

=2(62+8)

=2(70)

=140mts

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