Assignment - Herons Formula, Class 9 Mathematics PDF Download

VERY SHORT ANSWER TYPE QUESTIONS :
1. Write the area of a triangle having 5 cm base and height 6 cm.

2. Write the area of an equilateral triangle whose side is 6 cm.

3. State Heron's Formula for area of a triangle.

4. In ΔABC, BC = a, CA = b and AB = c. Write the semiperimeter s.

5. Find the area of isosceles triangle ABC in which AB = AC = 5 cm and BC = 8 cm.

6. Find the area of an equilateral triangle having each side of length a cm.

7. Find the area of the triangle having three sides given as 5 cm, 6 cm and 7 cm.

SHORT ANSWER TYPE QUESTIONS :
1. A triangular park in a city has dimensions 100 m × 90 m × 110 m. A contract is given to a company for planting grass in the park at the rate of Rs. 4000 per hectare. Find the amount to be paid to the company. (Take √2 = 1.414) (one hectare = 10,000 m²)

2. There is a slide in a children park. The front side of the slide has ben painted and a message "ONLY FOR CHILDREN" is written on it as shown in figure. If the sides of the triangular front wall of the slide are 9 m, 8 m and 3 m, then find the area which is painted in colour.

3. The perimeter of a triangular park is 180 m and its sides are in the ratio 5 : 6 : 7. Find the area of the park.

4. A triangle has sides 35 mm, 54 mm and 61 mm long. What is its area. Find also the smallest altitude of the triangle.

5. The perimeter of a right triangle is 12 cm and its hypotenuse is of length 5 cm. Find the other two sides and calculate its area. Verify the result using Heron's Formula.

6. Using Heron's Formula, find the area of an isosceles triangle, the measure of one of its equal sides being a units and the third side 2b units.

7. The sides of a triangle are 39 cm, 42 cm and 45 cm. A parallelogram stands on the greatest side of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.

8. From a point in the interior of an equilateral triangle perpendiculars drawn to the three sides are 8 cm, 10 cm and 11 cm respectively. Find the area of the triangle to the nearest cm. (use √3 = 1.73)

9. A municipal corporation wall on road side has dimensions as shown in fig. The wall is to be used for advertisements and it yields an earning of Rs. 400 per m² in a year. Find the total amount of revenue earned in a year.

10. ABCD is a quadrilateral such that AB = 5 cm, BC = 4 cm, CD = 7cm, AD = 6 cm and diagonal BD = 5 cm. Prove that the area of the quadrilateral ABCD is 4(3 + √6 cm² ).

11. Find the area of the quadrilateral ABCD in which AB = 7 cm, BC = 6 cm, CD = 12 cm, DA = 15 cm and AC = 9 cm. (Take √110 = 10.5 approx.)

12. A rhombus has perimeter 64 m and one of the diagonals is 22 m. Prove that the area of the rhombus is 66 √15 m²

13. ABCD is a trapezium in which AB║CD ; BC and AD are non-parallel sides. It is given that AB = 75 cm, BC = 42 cm, CD = 30 cm and AD = 39 cm. Find the area of the trapezium.

14. OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the radius of the circle is 10 cm, find the area of the rhombus.

15. The cross-section of a canal is in the shape of a trapezium. If the canal is 12 m wide at the top and 8 m wide at the bottom and the area of its cross-section is 84 m², determine its depth.

16. Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA ; while the other through AC, CD and DA. Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m. CD = 15 m, DA = 28 m and ∠B = 90°, which group cleaned more area and by how much? Find the total area cleaned by the students.

17. Find the perimeter of a square, the sum of lengths of whose diagonals is 144 cm.

18. Find the area of a quadrilateral piece of ground one of whose diagonals is 60 metres long and the perpendiculars from the other two vertices are 38 and 22 metres respectively.

LONG ANSWER TYPE QUESTIONS :
 

1. In figure, AB = 28 m, AC = 24 m, BC = 20 m, CG = 32 m, AG = 40 m and D is mid-point of AG. Find the area of the quadrilateral ABCD.

2. White and grey coloured triangular plastic sheets are used to make a toy as shown in fig. Find the total areas of white and grey coloured sheets used for making the toy.

3. Suman made an arrangement with white and black coloured paper sheets as showin in fig. Find the total areas of the white and black paper sheets used in making the arrangement.

4. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangular tiles are 26 cm, 20 cm and 10 cm. The tiles are polished at the rate of 20 p per cm2. Find the cost of polishing the tiles. (Take √14 = 3.74)

5. Suman made a picture with some white paper and a single coloured paper as shown in figure. White paper is available at her home and free of cost. The cost of coloured paper used is at the rate of 10 p per cm². Find the total cost of the coloured paper used. (Take √3 = 1.732 and √11 = 3.31)

6. In figure, P and Q are two lamp posts. If the area of the ΔPDC is same as that of the rectangle ABCD, find the distance between the two lamp posts.

7. A triangle and a parallelogram have same base and same area. If the sides of the triangle are 20 cm, 25 cm and 35 cm, and the base side is 25 cm for the triangle as well as the parallelogram, find the vertical height of the parallelogram.

8. A triangle and a parallelogram have a common side and are of equal areas. The triangle having sides 26 cm, 28 cm and 30 cm stands on the parallelogram. The common side of the triangle and the parallelogram is 28 cm. Find the vertical height of the triangle and that of the parallelogram.

9. A farmer has two triangular fields in the form of ΔABC and ΔACD in which the side AC is common as shown in figure. AB = 840 m, BC = 600 m, AC = 480 m, AD = 800 m and CD = 640 m. He has marked midpoints E and F on the sides AB and AD respectively. By joining CE and CF, he has made a field in the shape of quadrilateral AECF. He grew wheat in the quadrilateral plot AECF, potatoes in ΔCFD and onions in ΔBEC.
How much area has been used for each crop? (Take √6 = 2.45; one hectare = 10000 m²)

10. A field in the form of a quadrilateral ABCD whose sides taken in order are respectively equal to 192, 576, 288 and 480 dm has the diagonal equal to 672 dm. Find its area to the nearest square metre.

11. A trapezium with its parallel sides in the ratio 16 : 15 is cut from a rectangle whose sides measure 63 m and 5 m respectively. The area of the trapezium is 4/15 of the area of the rectangle. Find the lengths of the parallel sides of the trapezium

12. Find the cost, at Rs. 25 per 10 square metres, of turfing a plot of land in the form of a parallelogram whose adjacent sides and one of the diagonals measure 39 m, 25 m and 56 m respectively.