Find the area of a triangle whose sides are 18 cm, 24 cm, and 30 cm. Also, find the length of the altitude corresponding to the largest side of the triangle.
The length of the sides of a triangle is in the ratio 3: 4: 5. Find the area of the triangle if its perimeter is 144 cm.
ABC is a triangle in which AB = AC = 4 cm and A = 90° . Calculate:
(i) The area of ABC,
(ii) The length of the perpendicular from A to BC.
The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.
Find the area and the perimeter of quadrilateral ABCD, given below; if AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and DBC = 90°
The base of a triangular field is three times its height. If the cost of cultivating the field at 36.72 per 100 m2 is 49,572; find its base and height.
Each of equal sides of an isosceles triangle is 4 cm greater than its height. IF the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.
In triangle ABC; angle A = 90° , side AB = x cm, AC = (x + 5) cm and area = 150 cm2 . Find the sides of the triangle.
Find the area of a quadrilateral one of whose diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm respectively.
Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm A = 90o and BC = CD = 52 cm.
The perimeter of a rectangular field is 𝟑/ 𝟓 km. If the length of the field is twice its width; find the area of the rectangle in sq. meters.
The length and the breadth of a rectangle are 6 cm and 4 cm respectively. Find the height of a a triangle whose base is 6 cm and the area is 3 times that of the rectangle.
The diagram, given below, shows two paths drawn inside a rectangular field 80 m long and 45 m wide. The widths of the two paths are 8 m and 15 m as shown. Find the area of the shaded portion.
The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm; find:
(i) The length of its other diagonal,
(ii) Its area.
The figure given below shows the cross-section of a concrete structure. Calculate the area of crosssection if AB = 1.8 cm, CD = 0.6 m, DE = 0.8 m, EF = 0.3 m and AF = 1.2 m.
The following diagram shows a pentagonal field ABCDE in which the lengths of AF, FG, GH and HD are 50 m, 40 m, 15 m, and 25 m respectively; and the lengths of perpendiculars BF, CH and EG are 50 m, 25 m ad 60 m respectively. Determine the area of the field.
The area of a rectangular is 640 m2 . Taking its length as x cm; find in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.
ABCD is a square with each side 12 cm. P is a point on BC such that area of triangle ABP: area of trapezium APCD = 1: 5. Find the length of CP.
A wire when bent in the form of a square encloses an area = 576 cm2 . Find the largest area enclosed by the same wire when bent to form;
(i) an equilateral triangle.
(ii) A rectangle whose adjacent sides differ by 4 cm.
The area of a parallelogram is y cm2 and its height is h cm. The base of another parallelogram is x cm more than the base of the first parallelogram and its area is twice the area of the first. Find, in terms of y, h, and x, the expression for the height of the second parallelogram.
The radii of two circles are 48 cm and 13 cm. Find the area of the circle which has its circumference equal to the difference of the circumferences of the given two circles.
The diameters of two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to sum of the areas of the two given circles.
The radius of a circle is 5 m. find the circumference of the circle whose area is 49 times the area of the given circle.
The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 cm2, find the area of the smaller circle.
Find the area of a ring-shaped region enclosed between two concentric circles of radii 20 cm and 15 cm
The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width of 3.5 m. Find the area of the path.
Each wheel of a car is of diameter 80 cm. How many completer revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?
An express train is running between two stations with a uniform speed. If the diameter of each wheel of the train is 42 cm and each wheel makes 1200 revolutions per minute, find the speed of the train
In the given figure, the area of the shaded portion is 770 cm2. If the circumference of the outer a circle is 132 cm, find the width of the shaded portion.
Two circles touch each other externally. The sum of their areas is 58 cm2 and the distance between their centers is 10 cm. Find the radii of the two circles.
The perimeter of a triangle is 450 m and its side is in the ratio 12: 5: 13. Find the area of the triangle.
A triangle and a parallelogram have the same base and the same area. If the side of the triangle are 26 cm, 28 cm, and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Sum of the areas of two squares is 400 cm2 . If the difference of their perimeters is 16 cm, find the sides of the two squares.
A steel wire, when bent in the form of a square, encloses an area of 121 cm2 . The same wire is bent in the form of a circle. Find the area the circle.
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