>> Elementary Mathematics >> Area and perimeter

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Contents:

- Elementary Mathematics
- Area and perimeter
- Circles
- Clocks
- Factorisation
- Geometry
- Height and Distance
- Indices and Surd
- LCM and HCF
- Loci and concurrency
- Logarithms
- Polynomials
- Quadratic Equations
- Quadrilateral and parallelogram
- Rational expression
- Real Analysis
- Rectangular and Cartesian products
- Set theory
- Simple and Decimal fraction
- Simplification
- Statistics
- Straight lines
- Triangle
- Trigonometric ratio
- Trigonometry
- Volume and surface area

41). One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram ?
Area of parallelogram = \( \Large Base\times Height \) =\( \Large 8.06\times 2.08=16.76 cm^{2} \) | ||||

42). Floor of a square room of side 10 m is to be completely covered with square tiles, each having length 50 cm. The smallest number of tiles needed is
Area of square room = \( \Large (10)^{2} \) = 100 sq = \( \Large 100\times (100)^{2} \) sq cm = \( \Large 100\times 100\times 100 \) sq cm Now, area of tile = \( \Large (50)^{2}=50\times 50 \) sq cm Number of tiles needed = \( \Large \frac{Area \ of \ square \ room}{Area \ of \ tile} \) = \( \Large \frac{100\times 100\times 100}{50\times 50} \) =400 Hence, 400 tiles will be needed. | ||||

43). The area of a trapezium is \( \Large \Large 384 cm^{2} \). If its parallel sides are in the ratio 3 : 5 and the perpendicular distance between them is 12 cm, the smaller of the parallel sides is
Let the sides of trapezium be 5x and respectively. | ||||

44). In a trapezium, the two non-parallel sides are equal in length, each being of 5 units. The parallel sides are at a distance of 3 units apart. If the smaller side of the parallel sides is of length 2 units, then the sum of the diagonals of the trapezium is
In \( \Large \triangle BCF \), by Pythagoras theorem, \( \Large (5)^{2}=(3)^{2}+(BF)^{2} \) | ||||

45). The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 450 sq cm, find the sum of the lengths of the parallel sides.
Let the lengths of parallel sides an 3x and 2x. We know that, Area of trapezium = \( \Large \frac{1}{2} \) \( \Large (Sum \ of \ the \ parallel \ sides)\times Distance \ between \ them \) \( \Large \frac{1}{2}(3x+2x)15=450 \)=>75x=900 x=\( \Large \frac{900}{75} \)=12 cm Sum of the parallel sides = (3x + 2x) = 5x = \( \Large 5\times 12 \)=60 cm | ||||

46). If area of a regular pentagon is \( \Large \Large 125\sqrt{3} \) units sq cm, how long is its each side
We know that, Area of regular pentagon = \( \Large 5a^{2}\frac{\sqrt{3}}{4} \) According to the question, \( \Large \frac{5a^{2}\sqrt{3}}{4}=125\sqrt{3} \)=> \( \Large a^{2}=\frac{125\sqrt{3}\times 4}{5\sqrt{3}} \)=100 a = 10 cm | ||||

47). The sides of a parallelogram are 12 cm and 8 cm long and one of the diagonals is 10 cm long. If d is the length of other diagonal, then which one of the following is correct?
In parallelogram. | ||||

48). The radius of a circular field is 25 m. Find the area of the field.
Required area = \( \Large \pi r^{2}=\pi\times 25\times 25 \) = \( \Large \pi\times 25\times 25=625\pi sq m \) | ||||

49). A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. \( \Large ( \pi = 22/7) \)
Let the radius of the park be r, then | ||||

50). The area of a sector of a circle of radius 36 cm is \( \Large \Large 72\pi cm^{2} \). The length of the Corresponding are of the sector 1s
Given, area of sector = \( \Large 72\pi cm^{2} \) |