## Heron's Formula

*Assignment Sheet*

CLASS 9 - Maths

⒉ Find the cost of lying grass in a triangular field of sides 50m ,65 m, and 65 m at the rate of ₹ 7 per m²

⒊ From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10cm and 6 cm. Find the area of the triangle.

⒋ The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle.

⒌ The perimeter of a triangular field is 420 m and its sides are in the 6 : 7 : 8 . Find the area of triangular field.

⒍ The sides of a quadrilateral ABCD are 6 cm, 8cm , 12 cm and 14 cm respectively , and angle between the first two sides is a right angle. Find its area.

⒎ A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of ₹ 5 per m². Find the cost of painting.

⒏ If each side of a triangle is doubled , then find the ratio of area of the new triangle thus formed and the given triangle.

⒐ The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

⒑ The area of trapezium is 475 cm² and the height is 19 cm. Find the length of its two parallel sides if one side is 4 cm greater than the other.

⒒ A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws , a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.

⒓ A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs ₹ 4 to plough 1 m 2 of the field, find the total cost of ploughing the field.

⒔ The dimensions of a rectangle ABCD are 51 cm x 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9:8 is cut off from the rectangle. If the area of the trapezium PQCD is 5/6 th part of the area of rectangle, find the lengths of QC and PD.

⒕ A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonal is 80 cm long. Find the area of the parallelogram

Answers:

1. 2000

2. 10500

3. 300√3 cm²

4. 32 √2 cm²

5. 2100√15 m²

6. 24(√6+1) cm²

7. ₹ 960

8. 4:1)

9. 20√30 cm²

10. 23cm , 27 cm

11. 374cm²

12. ₹ 19200

13. 45 cm, 40 cm

14. 600√15m²

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