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Gyaan Maths
CBSE · Class 6-12
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Class 9 · Ganita Manjari
Unit 6 · Class 9Ganita Manjari
Measuring Space: Perimeter and Area
Heron's formula, areas of quadrilaterals, and mixed shapes.
Lessons
3 concepts
1
Heron's Formula
Compute semi-perimeter
s
s
s
. Then
A
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
A=\sqrt{s(s-a)(s-b)(s-c)}
A
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
. Powerful because no height needed.
2
Special Cases
For an equilateral of side
a
a
a
:
A
=
3
4
a
2
A = \tfrac{\sqrt 3}{4}a^2
A
=
4
3
a
2
. Derives from Heron.
3
Quadrilateral Area
Split a general quadrilateral into two triangles by a diagonal, apply Heron to each, and add.
Skills to practise
Skill · medium
Measuring Space: Perimeter and Area — Practice