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Areas Of Parallelograms And Triangles Class 9 Assignment Of Benefits


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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Big Ideas: Area is additive. The sum of the areas of rectangles and triangles within a polygon will equal the area of the polygon. The area of a parallelogram can be solved for by composing the parallelogram into a rectangle. This lesson builds on students’ work with solving for the areas of different polygons and quadrilaterals. This task presents students with an opportunity to apply their knowledge of finding the area of rectangles to finding the area of parallelograms. Students are presented with different parallelograms and by decomposing them, they discover that the area of a parallelogram can be found by decomposing it and then composing it into different shapes. By decomposing the parallelograms, students will see how the areas of parallelograms and rectangles are related. The mathematical concepts in this lesson build toward students’ future work with finding the areas of different two-dimensional figures by decomposing them into triangles and other shapes. Vocabulary: parallelogram, compose, decompose, base, height, rectangle, length, width, area, square units, right triangle Special Materials: Grid Paper Scissors Tape or Glue Supplemental Handout