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Mensuration - Area

Multiple Choice Questions

41.

In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is ( √3 = 1.732 )

98.55 sq cm
100 sq cm
101 sq cm
95 sq cm

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42.
Two sides of a plot measuring 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. The area of the plot in m² is

768

534

696.5

696.5

696.5

AC space equals space square root of AB squared space plus space BC squared end root space space space space space equals space square root of 32 squared space plus space 24 squared end root space space space space equals space square root of 1024 space plus space 576 end root space space space space equals space square root of 1600 space equals space 40 space metre

therefore space space space space space Area space of space increment ABC space space space equals space space 1 half cross times space BC space cross times space AB space space equals space 1 half space cross times space 24 space cross times space 32 space equals space 384 space sq. space metre space

Semi-perimeter of Δ ADC (s) =

fraction numerator 25 plus 25 plus 40 over denominator 2 end fraction equals space 90 over 2 space equals space 45 space metre

∴ Area of Δ ADC

equals space square root of straight s left parenthesis straight s minus straight a right parenthesis thin space left parenthesis straight s minus straight b right parenthesis thin space left parenthesis straight s minus straight c right parenthesis end root equals space square root of 45 left parenthesis 45 minus 25 right parenthesis thin space left parenthesis 45 minus 25 right parenthesis thin space left parenthesis 45 minus 40 right parenthesis end root equals space square root of 45 space cross times 20 space cross times space 20 space cross times space 5 end root space equals space 20 space cross times space 15 space equals space 300 space sq. space metre

∴ Area of the plot = 384 + 300 = 684 sq.metre

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43.

Perimeter of a rhombus is 2p unit and sum of length of diagonals is m unit, then area of the rhombus is

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44.

The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km?

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45.

The area of an equilateral triangle is $9 square root of 3 space straight m squared.$ The length (in m) of the median is

$2 square root of 3$
$3 square root of 3$
$3 square root of 2$
$3 square root of 2$

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46.

The diagonals of a rhombus are 12 cm and 16 cm respectively. The length of one side is

8 cm
6 cm
10 cm
10 cm

157 Views

47.

How many tiles, each 4 decimetre square, will be required to cover the floor of a room 8 m long and 6 m broad?

277 Views

48.

A lawn is in the form of a rectangle having its breadth and length in the ratio 3 : 4. The area of the lawn is $1 over 12 hectare$ . The breadth of the lawn is

25 metres
50 metres
75 metres
75 metres

346 Views

49.

The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth of the rectangle is $3 over 2$ times that of the side of the square. The side of the square, in cm, is

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50.

A square is of area 200 sq. m. A new square is formed in such a way that the length of its diagonal is $square root of 2$ times of the diagonal of the given square. Then the area of the new square formed is