>> 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

61). What is the total area of three equilateral triangles inscribed in a semi-circle of radius 2cm?
since, \( \Large \triangle's \) AOB,BOC,COD are equilateral. | ||||

62). How many circular plates of diameter d be taken out of a square plate of side 2d with minimum loss of material?
Area of square plate = \( \Large (Side)^{2} \) | ||||

63). What is the area of a circle whose area is equal to that of a triangle with sides 7 cm, 24 cm and 25 cm?
Given that, a = 7, b = 24 and c = 25 | ||||

64). A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is
Circumradius =\( \Large \frac{2}{3}\times Height \) Height =\( \Large \frac{10\times 3}{2} \)=15 cm So,length of perpendicular drawn from centre = 15 - 10 = 5 cm | ||||

65). AB and CD are two diameters of a circle of radius r and they are mutually perpendicular. What is the ratio of the area of the circle to the area of the triangle ACD?
Required ratio =\( \Large \frac{Area \ of \ circle}{Area \ of \ \triangle ACD} \) | ||||

66). The area of a rectangle is 1.8 times the area of a square. The length of the rectangle is 5 times the breadth. The side of the square is 20 cm. What is the perimeter of the rectangle?
Area of square =\( \Large (Side)^{2}=20^{2} \) = 400 sq cm | ||||

67). The side of a square is 5 cm which is 13 cm less than the diameter of a circle. What is the approximate area of the circle?
Diameter of the circle = 13 + 5 = 18cm Radius =\( \Large \frac{Diameter}{2}=\frac{18}{2} \)=9 cm. Area of the circle = \( \Large \pi r^{2}=\frac{22}{7}\times 9^{2} \) = \( \Large \frac{22\times 81}{7}=\frac{1782}{7} \)=254.57 sq cm. =255 sq cm. | ||||

68). If area of a square is 64 sq cm, then find the area of the circle formed by the same perimeter.
Area of square = 64 sq cm \( \Large (Side)^{2} \)= 64 Side = \( \Large \sqrt{64} \) = 8 cm According to the question, => \( \Large 2\pi r=4\times 8 \) => r=\( \Large \frac{4\times 8}{2\pi}=\frac{16}{\pi} \) Area of the circle =\( \Large \pi \times 16/ \pi\times 16/ \pi=\frac{256}{\pi} \)sq cm. | ||||

69). If area of a square is 64 sq cm, then find the area of the circle formed by the same perimeter.
ABCD be the rectangle inscribed in the circle of diameter 5 cm. | ||||

70). The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 72 cm and the length of the rectangle is 12 cm. what is the difference between the breadth of the rectangle and the Side of the square?
Perimeter of square = 72 cm |