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HERON’S FORMULA
1. If every side of a triangle is doubled, then increase in the area of the triangle is :
a. b. 200% c. 300% d. 400%
100 2 %
2. The perimeter of an equilateral is 60 m. The area is :
a. b. c. d. 10 3 π‘š
2
15 3 π‘š
2
20 3 π‘š
2
100 3 π‘š
2
3. The area of a triangle with base 4cm and height 6cm will be
a. 24 cm b 24 cm
2
c. 12 cm
2
d. None of the above
4. In triangle ABC base 12 cm and height = 5 cm its area is
a. 60 cm
2
b.30 cm
2
c. 45 cm
2
d. None of these
5. What is the length of each side of an equilateral triangle having an area of .
9 3 π‘π‘š
2
a. 4 cm b. 5 cm c. 3cm d. 6 cm
6. The length of three sides of a triangle 20cm, 16cm and 12cm. The area of a triangle is :-
a. b. c. d.
96 π‘π‘š
2
120 π‘π‘š
2
144 π‘π‘š
2
160 π‘π‘š
2
7. The area of an equilateral triangle is . Its side is :-
9 3 π‘π‘š
2
a. b. c. d.
9 3 π‘π‘š 6 3 π‘π‘š 36 π‘π‘š 6 π‘π‘š
8. The area of an isosceles triangle having base x cm and one the equal side y cm is
a. b. c. d.
π‘₯
2
βˆ’ 𝑦
2
2
π‘π‘š
2
π‘₯
2
𝑦
2
βˆ’
π‘₯
2
2
π‘π‘š
2
π‘₯
2
4 𝑦
2
βˆ’ π‘₯
2
4
π‘π‘š
2
π‘₯ 4 𝑦
2
βˆ’ π‘₯
2
π‘π‘š
2
9. The area of an equilateral triangle is then its semi-perimeter will be
81 3 π‘π‘š
2
,
a. 18cm b. 36cm c. 24cm d. 27cm
10. The sides of a triangle are 18cm, 15cm and 17cm. Find its area.
11. The base and hypotenuse of a right triangle are 4cm and 5cm respectively. Find its area.
12. The length of sides of a triangle are 7cm, 12cm and 13cm. Find the length of altitude
drawn on the side of length 12cm.
13. Shanvi is very fond of sceneries. She has decorated her home with many beautiful
sceneries in various shapes. One of her friends visited her house and was impressed to
see the triangular scenery there. The dimensions of each triangular frame are 40cm, 50
cm and 50 cm.
a. Find the length of the boundary of each frame.
b. What will be the length of the perpendicular drawn on the side of 40 cm?
c. Find the area of each triangular frame.
d. Find the cost of each triangular frame at the rate of Rs. 5 per cm
2
.
14. The sides of a triangular plot are in the ratio of 5:12:13 and its perimeter is 150m. Find
its area.
15. An isosceles triangle has a perimeter 30cm and each of equal sides is 12cm. Find the
area of the triangle.
16. The triangular side walls of a flyover have been used for advertisements. The sides of
the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of 2000 per m
2
per year. A company hired one of its walls for 6 months. How much rent did it pay?
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17. The sides of a triangular plot are in the ratio of 6:7:8 and its perimeter is 420 m . Find its
area.
18. A field is in the shape of a trapezium whose parallel sides are 60 m and 77 m. The
non-parallel sides are 25 m and 26 m. Find the area of the field.
19. Students of a School staged a rally for the cleanliness campaign. They walked through
the lanes in two groups. One group (Group A) walked through the lane AB, BC, CA ;
while other group (Group B) through AC, CD, DA (as shown in the fig.). Then they
cleaned the area enclosed within their lanes. If AB = 9m, BC = 40m, CD = 15m, DA =
28m, ∠B = 90⁰. Which group cleaned more area and by how much? Find the total area
cleaned by the students.
20. Find the area of the triangle whose sides are 91 m, 98 m and 105 m in length. Find the
height corresponding to the longest side.
21. The perimeter of an isosceles triangle is 32 cm. The ratio of equal sides to its base is
3:2. Find the area of the triangle.
22. Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area.
23. The sides of a triangle are 35 cm, 54 cm and 61 cm respectively, find the area of the
triangle. Also find the length of its longest altitude.
24. The sides of the triangular field are 41 m, 40 m and 9m. Find the number of rose beds
that can be prepared in the field, if each rose bed on an average needs 900cm
2
space.