N |
Shape |
Perimeter/height |
Area |
1 |
Right angle triangle Base =b, Height =h Hypotenuse=d |
$P=b+h+d$ Height =h |
$A=\frac {1}{2}BH$ |
2 |
Isosceles right angled triangle Equal side =a |
$P= a(2+ \sqrt 2)$ |
$A=\frac {1}{2} a^2$ |
3 |
Isosceles triangle Equal side =a and base as b |
$P= 2a +b $ |
$A=\frac {1}{2} a \sqrt {a^2 - \frac {b^2}{4}}$ |
4 |
Any Triangle Any triangle of sides a,b ,c |
$P=a+b+c$ |
$A=\sqrt {s(s-a)(s-b)(s-c)}$ $s=\frac {a+b+c}{2}$ This is called Heron's formula (sometimes called Hero's formula) is named after Hero of Alexandria |
5 |
Square Side =a |
P=4a |
$A=a^2$ |
6 |
Rectangle of Length and breath L and B respectively |
$P=2L +2B$ |
$A=L \times B$ |
7 |
Parallelograms Two sides are given as a and b |
$P=2a+2b$ |
$A= Base \times height$ When the diagonal is also given ,say d Then $A= \sqrt {s(s-a)(s-b)(s-d)}$ $s=\frac {a+b+d}{2}$ |
8 |
Rhombus Diagonal d_{1} and d_{2} are given |
$p=2 \sqrt {d_1^2+d_2^2}$ Each side=$ \frac {1}{2} \sqrt {d_1^2+d_2^2} $ |
$A=\frac {1}{2} d_1 d_2$ |
9 |
Quadrilateral a. All the sides are given a,b,c ,d b. Both the diagonal are perpendicular to each other c. When a diagonal and perpendicular to diagonal are given |
a. $P=a+b+c+d$ |
a. $A=\sqrt {s(s-a)(s-b)(s-c)(s-d)}$ $s=\frac {(a+b+c+d)}{2}$ b. $A=\frac {1}{2} d_1 d_2$ where d_{1} and d_{2 } are the diagonal c. $A=\frac {1}{2} d(h_1+h_2)$ where d is diagonal and h_{1} and h_{2} are perpendicular to that |
If you know the altitude and Base |
$A =\frac {1}{2}BH$ |
If you all the three sides |
$A=\sqrt {s(s-a)(s-b)(s-c)}$ $s=\frac {a+b+c}{2}$ |
If it is isosceles right angle triangle with equal side a | $A=\frac {1}{2}a^2$ |
If it is isosceles triangle with equal side a and other side as | $A=\frac {1}{2} a \sqrt {a^2 - \frac {b^2}{4}}$ |
If it is equilateral triangle with equal side a | $A=\frac {a^2 \sqrt 3}{4}$ |
If it is right angle triangle with Base B and Height H | $A =\frac {1}{2}BH$ |
Given below are the links of some of the reference books for class 9 Math.
You can use above books for extra knowledge and practicing different questions.
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