Page 253 - Start Up Mathematics_7

Example 38: Find the area of the quadrilateral ABCD, in which BM AC, DN AC, AC = 20 cm,
BM = 3 cm and DN = 2 cm. B
1
Solution: Area of ∆ ABC = × AC × BM
2
1
= × 20 × 3 = 30 cm 2 3 cm
2
1 N 20 cm
Area of ∆ ADC = × AC × DN A M C
2
1 2 cm
= × 20 × 2 = 20 cm 2
2
Area of quadrilateral ABCD = ar(∆ ABC) + ar(∆ ADC) D
= 30 + 20 = 50 cm 2

2
Example 39: The area of a rhombus is 72 cm . If its perimeter is 36 cm, find its altitude.
Solution: Let a be the side and h be the altitude of the rhombus.
a
Perimeter of the rhombus = 36 cm
⇒ 4a = 36 cm ⇒ a = 9 cm a h a

Area of the rhombus = 72 cm 2
⇒ Base × altitude = 72 cm 2 a
72
⇒ a × h = 72 ⇒ 9 × h = 72 ⇒ h = = 8 cm
9

EXERCISE 14.4

1. A rectangular lawn of length 50 m and breadth 30 m is to be surrounded externally by a
path which is 2 m wide. Find the area of the path.
2. Two crossroads, each 2 m wide, run at right angles through the centre of a rectangular
park of length 64 m and breadth 38 m, such that each is parallel to one of the sides of the
rectangle. Find the area of the roads. Also, find the area of the remaining part of the park.

3. A rectangular plot measures 300 m by 200 m. A builder builds three roads 10 m wide along
the length on either side and one in the middle. He also builds one 10 m wide road in the
middle along the breadth. The remaining area is cut into residential plots and sold at the rate of
2
` 500 per m . Calculate the total revenue the builder will generate by selling all the plots.
4. A rectangular park has dimension 90 m by 70 m. Two paths run parallel to the lengths of
the rectangle and two paths run parallel to its breadths. The two paths along the length are
7 m wide and the other two along the breadth are 5 m wide. Find the area of:

(a) all the paths

(b) the remaining portion of the park
5. The dimensions of a rectangular plot are 35 m by 20 m. A path of uniform width 2 m is
built along the border and inside it. Find the cost of paving the path with bricks at ` 25 per
square metre and also the cost of covering the remaining part of the plot with grass at
` 19 per square metre.

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