Areas Of Parallelograms And Triangles Class 9 Assignment Of Contract

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.

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SHORT ANSWER TYPE QUESTIONS :

1. In the adjoining figure, BD is a diagonal of quad. ABCD. Show that ABCD is a parallelogram and calculate the area of || gm ABCD.

2. In a || gm ABCD, it is given that AB = 16 cm and the altitudes corresponding to the sides AB and AD are 6 cm and 8 cm respectively. Find the length of AD.

3. Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.

4. In the given figure, the area of II gm ABCD is 90 cm2. State giving reasons :
(i) ar ( ||gm ABEF) (ii) ar (ΔABD) (iii) ar (ΔBEF).

5. In the given figure, the area of ΔABC is 64 cm2. State giving reasons : (i) ar ( || gm ABCD) (ii) ar (rect. ABEF)

6. In the given figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Prove
that : ar (ΔABP) = ar (quad. ABCD).

7. Answer the following questions as per the exact requirement:

(i) ABCD is a parallelogram in which AB║CD and AB = CD = 10 cm. If the perpendicular distance between AB and CD be 8 cm, find the area of the parallelogram ABCD.

(il) ABCD is a parallelogram having area 240 cm2, BC = AD = 20 cm and BC║AD. Find the distance between the parallel sides BC and AD. '

(iii) ABCD is a parallelogram having area 160 cm2, BC║AD and the perpendicular distance between BC and AD is 10 cm. Find the length of the side BC.

(iv) ABCD is a parallelogram having area 200 cm2. If AB║CO, P is mid-point of AB and Q is mid-point of CD, find the area of the quadrilateral APQD.

(v) ABCD is a parallelogram having area 450 cm2. If AB║CD, points P and Q divide AB and DC respectively in the ratio 1 : 2, find the area of the parallelogram APQD and parallelogram PBCQ.

8. In fig, ∠AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of ΔAOB.

9. In fig, ABCD is a trapezium in which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and distance between AB and DC is 4 cm. Find the value of x and area of trapezium ABCD.

10. In fig, OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If OE =2 5 , find the area of the rectangle.

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