## Saturday, July 21, 2012

### ASSIGNMENT, 2012-13 Class : IX, Sub : Maths TOPIC : Heron’s Formula & Co-ordinate Geometry

TOPIC : Heron’s Formula

1. Find the area of the triangle whose sides are 13cm, 14cm and 15cm.

2. Prove that the length of the altitude of an equilateral triangle of side ‘a’ is √3/2a

3. The sides of a triangular field are 120m, 160m & 200m. Find the cost of ploughing it at the cost of 25 paise per square m.

4. The length of sides of a right angled triangle forming the right angle are 5x cm and (3x – 1) cm. If the area of the triangle is 60 cm2, find its all sides.

5. Find the perimeter of an isosceles right angled triangle having area 200 cm2.

6. Find the area of a quadrilateral ABCD in which AB = 3cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5cm.

7. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26cm, 28cm and 30cm, and parallelogram stands on the base 28cm, find the height of the parallelogram.

8. A field is in the shape of trapezium whose parallel sides are 25m and 10m. The non-parallel sides are 14m and 13m. Find its area.

9. A rectangular has twice the area of square. The length of rectangle is 12 cm longer and the width is 8cm longer than the sides of the square. Find the area of the square.

10. The adjacent sides of a parallelogram are 125 mm and 62.5 mm. If one altitude of parallelogram is 0.025m, find the other altitude in cm.

11. The diagonals of a rhombus are whose 15 and 36 cm long. Find its perimeter.

12. Find the percent increase in the area of an equilateral triangle if its each of the side is doubled.

13. Find the area of an equilateral triangle whose each side is ‘a’.

14. Find the area of ABCD in which AB = 9m, BC = 40m, CD = 15m and AD = 28m and angle ABC is 90o.

15. The area of an equilateral triangle is cm2. Find its perimeter.

16. Find the area of an isosceles triangle whose each of equal side is ‘a’ and the other side is ;b;.

17. Find the area of triangle two sides of which are 18cm and 10cm and perimeter is 42cm.

18. The sides of triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

19. Find the area of an equilateral triangle whose each side is 30m.

20. Find the area of a triangle whose sides are 122m , 22m and 120m respectively.

Co-Ordinate Geometry

1. In which quadrant point lie if

(i) The coordinates are (-1,3)

(ii)The coordinates are (2,-5)

(iii)The coordinates are (7,-2

(iv) The coordinates are(2,-4)

2. Draw the quadrilateral whose vertices are (-5,3),(2,-3),(-7,7)&(5,7)

3. Which of the following point lie on any -axis (2,3) (3,0) (5,0)&(0,-5)

4. Mark the point(5,3), (-5,3) & (2,-6) and join them in order and name the figure.

5. Mark the coordinates on graph paper (-4,0), (2,0), (4,3) & (-2,3) and find area of specific figure formed.

6. Mark the points A(2,0), B(2,2), C(0,2) on graph paper. Join OB, BC and OC. Name the figure and find its area.

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2. Find the area of quadrilateral ABCD whose sides are 9m,40m.28m and 15m is.................
Let AB =9 m, BC=40m, CD= 28m and DA = 15m
In quad. ABCD, join diagonal AC
Take a look at the lengths of the sides given closely. You will see that 92 + 402 = 412. (Pythgorean triplets) So in trainagle ABC, AB and BC are two sides of a right triangle with Angle ABC =90 deg with its diagonal being AC. Apply pythagoras theorem for triangle ABC to get AC = 41cm.
Now we find two triangles ABC and ACD with sides already known. Apply Heron 's formula to get the areas of the two triangles. (Alternately, area of triangle ABC can be found more easily since BC is the height and AB is the base.)
Area of ABC = 180 cm2. Area of ACD = 126 cm2.
Simply sum the two areas to get the total area to be 306 cm2.