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HERON’S FORMULA
BASIC CONCEPT
1
Various formulae related to triangle
For right angled triangle, whose base is b and height is h.
Area of right angled triangle =
2
1
 Base  Height
2
For equilateral triangle, whose all three sides are equal to a
3 2
a
4
3
a
Altitude of equilateral triangle =
2
Area of equilateral triangle =
3
For isosceles triangle, whose two equal sides are a and base side is b.
Area of an isosceles triangle =
4
HERON’S FORMULA : For a triangle whose three sides are a, b and c are given.
Area of triangle =
5
6
7
8
abc
2
Diagonal of rectangle = l 2  b 2
For square, whose side is a, then
Area of square of = a2
Perimeter of square = 4a
Diagonal of square = 2a
For a parallelogram
Area of parallelogram = Base  Height
Perimeter of parallelogram = 2 (l + b)
For a rhombus, whose diagonals are d 1 and d2 and equal side a.
1
 d1  d 2
2
Perimeter of rhombus = 4a
For a trapezium, whose parallel sides are a and b and the distance between two parallel
sides is h,
Area of trapezium =
10
s ( s  a ) ( s  b) ( s  c ) where s 
Various formulae related to quadrilateral
For a rectangle, whose length is l and breadth is b.
Area of rectangle = l × b
Perimeter of rectangle = 2 (l+b)
Area of rhombus =
9
b 4a 2  b 2
4
1
1
 Sum of parallel sides  height = (a  b)  h
2
2
For a regular hexagon, whose sides is a,
Area of hexagon = 6 
3 2 3
a 
3a 2
4
2
ASSIGNMENT
1
The sides of a triangle are in the ratio 3:5:7 and its perimeter is 300 m. Find its area.
2
3
The sides of a triangle are x, x+1, 2x – 1 and its area is x 10 . Find the value of x.
The sides of a triangular park are 8 m, 10 m and 6m respectively. A small circular area of
diameter 2 m is to be left out and the remaining area is to be used for growing roses.
How much area is used for growing roses? [Take  = 3.14]
Two parallel sides of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26
cm. Find the area of the trapezium.
The length of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144 cm.
Find area of the triangle and
(ii)
Find height corresponding to the longest side.
4
5
(i)
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1
VIKAS GUPTA (9810929414)
RANKERS MATHS ACADEMY, C-6/75 YAMUNA VIHAR, VIKAS GUPTA :- 9810929414
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The base of an isosceles triangle measures 24 cm its area is 192 cm 2. Find its perimeter.
In a four sided field, the length of the longer diagonal is 128 m. The length of the
perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 17.3 m. Find
the area of the field.
The area of a trapezium is 475 cm2 and the height is 19 cm. find the lengths of its
parallel sides, if one side is 4 cm greater than the other.
Sanya has a piece of land which is in the shape of a rhombus. She wants her one
daughter and one son to work on the land and produce different crops. She divided the
land in two equal parts. If the perimeter of the land is 400 m and one of the diagonal is
160 m, then how much area each of them will get for their crops?
Kamla has a triangular field with sides 240 m, 200 m and 360 m, where she grew wheat.
In other triangular field with sides 240 m, 320 m and 400 m adjacent to the previous
field, she wanted to grow potatoes and onions. She divided the field in two parts by
joining the mid-point of the longest side to the opposite vertex and grew potatoes in one
part and onions in the other part. How much area (in hec) has been used for wheat,
potatoes and onions? [1 hec = 10000 m2, 2  1.414 ]
From a point in the interior of an equilateral triangle, perpendicular are drawn on three
sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the
triangle.
A
How much paper of each shade is
needed to make a kite given in figure,
in which ABCD is a square with diagonal
I
II
44 cm and an isosceles triangle whose
equal side is 20 cm and base 14 cm.
D
B
The sides of a triangle are 13 cm, 14 cm
III
and 15 cm. Then, find the area of the triangle.
I
The sides of a triangular ground are 5 m, 7 m
and 8 m, respectively. Find the cost of leveling
the ground at the rate of Rs 10 per m2.
C
The length of the two sides of a right angled triangle
containing the right angle differ by 2 cm. If the area
of the triangle is 24 cm2, then find the perimeter of
II
Q
the triangle.
P
Calculate the area of the triangle whose sides are 18 cm, 24 cm and 30 cm in length.
Also, find the length of the altitude corresponding to the smallest side.
A field is the form of a parallelogram has sides 60 m and 40 m and one of its diagonal is
80 m long. Find the area of the parallelogram.
A garden is in the shape of a quadrilateral. The sides of the garden are 9 m, 40 m, 28 m
and 15 m respectively in consecutive order and the angle between first two sides is a
right angle. Find the area of the garden.
A triangle and a parallelogram have the same base and the same area. If the sides of the
triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the base 15 cm.
Then find the height of the parallelogram.
ANSWER
1
1500 3 m 2
11
300 3 cm 2
2
3
4
5(i)
6
7
8
9
10
x=6
20.86 m2
1644 cm2
864 cm2, (ii) 28.8 cm
64 cm
2560 m2
23 cm, 27 cm
4800 m2
2.26 hec, 1.92 hec, 1.92 hec.
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13
14
15
16
484 cm2, 242 cm2, 242  21 39 cm2
84 cm2
Rs173
24 cm
216 cm2, 24 cm
17
600 15 m 2
18
19
306 m2
5.6 cm
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2
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