Mathematics Question Bank SA - 1 - CBSE (CCE)
12
HERON'S FORMULA
EXERCISE 12.1
Topics :
Area of Triangle - by Heron's Formula.
Application of Heron's Formula in finding Areas of Quadrilaterals.
2 MARKS
1.
There is a slide in a park. One of its side walls is painted red with the message, “Dogs
are not allowed in the park”. If the sides of the wall are 6m, 8m and 10m, find the cost
of painting in red at the rate of ` 10 per m2. (2014)
Ans. Since the sides of the triangle are 6 cm, 8 cm and 10 cm, it forms a right triangle.
A
1
bh
2
1
6m
x 8 x 6 = 24 m2
=
2
∴ cost of painting = 24 x 10 = ` 240
B
2.
∴ar(∆ABC)=
10 m
30o
C
8m
Find the area of a rhombus whose one side is 20 m and one diagonal is 24m.
(2014)
Ans. In a rhombus diagonals bisect perpendicular.
∴ In ∆DOC, OD = √202 - 122 = √400 - 144 = √256 = 16
∴ Diagonal BD = 16 + 16 = 32 m
1
dd
2 1 2
1
x 24 x 32 = 386 m2
=
2
A
20 m
D
20 m
B
12 m
O
20 m
12 m
C
Now area of rhombus =
3.
Using Heron's formula, calculate the area and altitude of an equilateral triangle of side
80cm. (use √3 = 1.73) (2014)
Ans. -251-
Ar (∆ABC)=
20 m
√3 2
a
4
TEACHERS FORUM
Mathematics Question Bank SA - 1 - CBSE (CCE)
√3
x 80 x 80
4
= 1600 √3 = 1600 x 1.73
= 2768 cm2
=
1
bh
Ar(∆ABC)=
2
1
i.e., 2768 =
x 80 x h
2
2768 x 2
⇒ h =
= 69.2 cm
80
4.
A
80cm
B
80cm
D
80cm
C
In the figure, ABCD is a square of side 4 cm. E and F are mid-points of AB are AD
respectively. Find the area of the shaded region.
(2014)
D
C
F
A
B
E
Ans. Area of the shaded region = Area of square - Ar(∆AEF)
1
x2x2
= (4)2 2
= 16 - 2 = 14 cm2
5.
The sides of a triangle are 18 cm, 20 cm and 22 cm. Find its area. (2014)
a + b +c
2
18 + 20 + 22 60
=
= 30
=
2
2
Area of triangle = √s(s - a)(s - b)(s - c)
Ans. s=
=√30(30 - 18)(30 - 20)(30 - 22)
=√30 x 12 x 10 x 8
=√6 x 5 x 6 x 2 x 5 x 2 x 4 x 2
= 6 x 5 x 2 x 2 √2 = 120√2 cm2
6.
Sides of a triangle are 70 cm, 80 cm and 90 cm. Find its area. (use √5 = 2.23) (2014)
Ans. S=
70 + 80 + 90 240
=
= 120
2
2
∴ Area = √120(120 - 70)(120 - 80)(120 - 90)
= √120 x 50 x 40 x 30
= 100√12 x 5 x 4 x 3
= 1200 √5 = 1200 x 2.23 = 2676 cm2
-252-
TEACHERS FORUM