IIT Foundation Mathematics Problems on Area and Perimeter

Q.1. If the sides of a triangle are 3 cm, 4 cm and 5 cm, then what is the radius of the circum-circle?

Answer

Answer: 2.5 cm

Q.2. If the length of hypotenuse of a right angled triangle is 5 cm and its area is 6 sq cm, then what are the lengths of the remaining sides?

Answer

Answer: The two sides are 4 cm and 3 cm.

Q.3. ACB is an arc of a circle of radius 3 cm. It subtends an angle of 120º at the centre as shown in the figure. What is the area of the shaded portion ACB?

Answer

Answer:

Q.4. There are two concentric hexagons. Each of the side of both the hexagons are parallel. Each side of internal regular hexagon is 8 cm. What is the area of the shaded region, if the distance between the corresponding parallel sides is 2√3 cm?

Answer

Answer: 120√3 cm²

Q.5. ΔABC is an isosceles right angled triangle. If r is its in radius and R its circum radius, then what is R/r equal to?

Answer

Answer: 1 + √2

Q.6. In a right-angled triangle ABC, D is the foot of the perpendicular from B on the hypotenuse AC. If
AB = 3 cm and BC = 4 cm, what is the area of ΔABD?

Answer

Answer: 54/25 cm²

Q.7. A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle ?

Answer

Answer: 14.365

Q.8. A square and a rhombus have the same base. If the rhombus is inclined at 60º, find the ratio of the area of the square to the area of the rhombus.

Answer

Answer: 2√3 :3

Q.9. The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. Find the area (in sq. cm) of this triangle.

Answer

Answer: 72

Q.10. A goat is tethered to one end of a rope of length 20m, while the other end is fixed at the centre of a large circular field. There is a square elevated platform with sides of 10 m on the field such that one corner of the elevated square platform coincides with centre of the circular field. If the goat is unable to mount the square elevated platform, what is the total area the goat will be able to graze?

Answer

Answer: 3.5 × 100π