Q1.A triangular grassy park, with side lengths 11 m, 6 m, and 15 m, has the message “KEEP THE PARK GREEN AND CLEAN” written on it. What is the semi-perimeter of the park?
Q4.The area of a triangular wall used for advertisement is 1320 m². The rate is ₹5000 per m² per year. A company hires it for 3 months. What is the rent paid?
A₹6,60,000
B₹13,20,000
C₹16,50,000
D₹19,80,000
Q5.A triangular field ABC has sides 120 m, 80 m, and 50 m. Find the cost of fencing it with barbed wire at the rate of ₹20 per metre, leaving a 3 m space for a gate on one side.
Q7.If the area of the triangle using the formula: \( \frac{1}{2} \) x base x height is 100 \( m^2 \), what will be the area of the triangle using the Heron's formula?
A50 \(m^2 \)
B100 \(m^2 \)
C1000 \(m^2 \)
D10000 \(m^2 \)
Q8.One side of an equilateral triangle is "a". What is the semi-perimeter of the triangle?
Q21.A triangle and a parallelogram have the same base and the same area. If the area of the triangle is 336 cm² and the parallelogram stands on a base 28 cm, then what is the height of the parallelogram?
A12 cm
B24 cm
C6 cm
D48 cm
Q22.The height of an equilateral triangle is 6 cm. Find its side?
A\(\text{ } \sqrt{3} \) cm
B2\(\text{ }\sqrt{3} \) cm
C3\(\text{ }\sqrt{3} \) cm
D4\(\text{ }\sqrt{3} \) cm
Q23.An isosceles triangle has a perimeter of 30 cm, and each of its equal sides measures 12 cm. Find the length of the third side.
A24 cm
B15 cm
C6 cm
D12 cm
Q24.In a right-angled triangle ABC, AB = 5 cm, AC = 12 cm, and BC = 13 cm. What is the area of Δ ABC?
Q29.A triangular park has sides measuring 100 m, 75 m, and 65 m. A gardener plans to put a wire fence all around the park, leaving a gap of 4 m on one side for a gate. What is the total length of wire required for fencing?
Q31.The semi-perimeter (s) of triangle with sides 40 m, 24 m, and 32 m is:
A48 m
B96 m
C56 m
D24 m
Q32.The semi-perimeter of a triangle is 48 m. The value of s−a, where a=40 m, is:
A16 m
B8 m
C24 m
D12 m
Q33.A triangle has sides measuring 40 m, 24 m, and 32 m. What is the value of s−b, where b = 24 m?
A8 m
B16 m
C12 m
D24 m
Q34.The semi-perimeter(s) of a triangle is 48 m. The value of s−c, where c=32 m, is
A8 m
B24 m
C16 m
D48 m
Q35.The sides of a triangular park ABC are 40 m, 24 m, and 32 m. It is observed that \( 32^2 \) + \( 24^2 \) = \( 40^2 \). Based on this information, what type of triangle is formed by the park?
Q42.The perimeter of a triangular field is 420 m, and its sides are in the ratio 6 : 7 : 8. Which of the following represents the lengths of its sides?
A120 m, 140 m, 160 m
B100 m, 120 m, 200 m
C90 m, 140 m, 190 m
D110 m, 130 m, 180 m
Q43.A craftsman is decorating a triangular board with sides 6 cm, 8 cm, and 10 cm. He wants to cover all its edges with tape. What is the total length of tape needed?
Q44.A farmer owns a field in the shape of a parallelogram with sides 60 m and 40 m. A diagonal of length 80 m divides the field into two triangular regions. If the area of one triangular region is 300 \(\sqrt{3} \) \( m^2 \), what is the total area of the field?
Q45.The sides of the triangular field are 50 m, 65 m, and 65 m, and its area is 1500 \( m^2 \). If the cost of laying grass is ₹7 per \( m^2 \), find the total cost of covering the field with grass.
Q55.The perimeter of a triangular field is 540 m, and its sides are in the ratio 12:17:25. If the cost of fencing is ₹30 per metre, what is the total cost of fencing the field?
Q58.A gardener wants to prepare rose beds in a triangular garden whose sides measure 15 m, 8 m, and 17 m. If each rose bed, on average, requires 4 m² of space, find the number of rose beds that can be prepared in the garden.
Q59.The sides of a triangle are 9 cm, 12 cm, and 15 cm. Which of the following sides is the hypotenuse of the triangle?
A9 cm
B12 cm
C15 cm
D21 cm
Q60.A triangle whose sides measure 12 cm, 16 cm, and 20 cm is divided into square sections of area 8 \( cm^2 \) each. What is the maximum number of sections that can be made?
Q62.A farmer has a triangular field with a total boundary length of 360 m. He wants to fence the entire field. The fencing company charges ₹55 per metre for fencing. Help the farmer find the total amount he must pay.
Q65.The area of a triangular wall used for advertisement is 600 m². The advertising rate is ₹50 per m² per month. Find the total rent to be paid for one month.
Q66.The perimeter of an equilateral triangle is 60m. Then its area is
A10\( \sqrt{3} \)\( m^2 \)
B15\( \sqrt{3} \)\( m^2 \)
C20\( \sqrt{3} \)\( m^2 \)
D100\( \sqrt{3} \)\( m^2 \)
Q67.Assertion (A): The area calculated using Heron's formula is always positive.
Reason (R): The area obtained from Heron's formula is always an integer.
ABoth A and R are true and R is the correct explanation of A
BBoth A and R are true but R is not the correct explanation of A
CA is true, but R is false
DA is false but R is true
Q68.Assertion (A): If the semi-perimeter of a triangle is equal to the length of one of its side, the the area of a triangle is zero.
Reason (R): This is because the triangle collapses into a straight line.
ABoth A and R are true and R is the correct explanation of A
BBoth A and R are true but R is not the correct explanation of A
CA is true, but R is false
DA is false but R is true
Q69.The sides of a triangle are a, b, and c. If each side is doubled, then what will be the correct expression for the semi-perimeter of the new triangle?
Aa+b+c
B2(a+b+c)
C\(\frac{(a+b+c)}{2} \)
D\(\frac{(a+b+c)}{4} \)
Q70.The area of a triangle with sides a, b, and c is given by \(\sqrt{s(s−a)(s−b)(s−c)} \). If each side is doubled, then which of the following is the correct formula for the area of the new triangle
A\(\sqrt{s(s−a)(s−b)(s−c)} \)
B2\(\sqrt{s(s−a)(s−b)(s−c)} \)
C4\(\sqrt{s(s−a)(s−b)(s−c)} \)
D\(\frac{1}{2} \) \(\sqrt{s(s−a)(s−b)(s−c)} \)
Q71.In the given figure, the area of triangle ABC is 84 \( cm^2 \). What is the area of the shaded region ACBD?
Q72.A scenery in the form of an equilateral triangle is displayed on the wall of a room. Its sides measure 40 cm each. What is the area of the scenery?
Q73.A person purchased a plot of land and divided the land into three parts: a warehouse, an inventory section, and a canteen, as shown in the figure. Find the cost of tiling the canteen floor at the rate of ₹500 per \( m^2 \).
Q74.In the given figure, △ABC is an equilateral triangle with each side equal to a. Which of the following represents the area of △ABC?
A\(\frac{3}{4} \) \( a^2 \)
B\(\frac{\sqrt{3} }{4} \) \( a^2 \)
C\(\frac{\sqrt{3} }{2} \) \( a^2 \)
D\(\frac{3}{2} \) \( a^2 \)
Q75.For the Annual Day function of the school, 200 triangular flags of sides 25 cm, 25 cm, and 14 cm were to be prepared. If the area of one flag is 168 \( cm^2 \), how much cloth will be required for all the flags in \( m^2 \)?
Q83.The perimeter of a triangle is 50 cm. One side of the triangle is 4 cm longer than the smallest side and the third side is 20 cm. Find the area of the triangle.
