Perimeter and Area of Plane Figures

Triangle

Let a, b, c denotes the sides of the Triangle. Then:

1.       Perimeter = a + b + c

2.       Semi-Perimeter (s) = \frac{1}{2} (a + b + c)

3.       Area = \sqrt{s(s-a)(s-b)(s-c)}

4.       Area = \frac{1}{2} \times Base \times Height = \frac{1}{2} bh

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Right-angled Triangle

Let b be the base, h be the height (or perpendicular) and a be the Hypotenuse. Then,

1.       Perimeter = a + b + h

2.       Area = \frac{1}{2} \times Base \times Height = \frac{1}{2} bh

3.       Hypotenuse = \sqrt{b^2 + h^2}

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Isosceles Right – angled triangle

Let the equal sides be a .

1.       Hypotenuse = \sqrt{a^2+a^2} = \sqrt{2} a

2.       Perimeter = 2a + \sqrt{2}a

3.       Area = \frac{1}{2} \times Base \times Height = \frac{1}{2} a^2

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Equilateral Triangle

Let each of the side is a . Then

1.       Perimeter = 3a

2.       Height = \frac{\sqrt{3}}{2} a

3.       Area = \frac{1}{2} \times Base \times Height = \frac{1}{2} a \times \frac{\sqrt{3}}{2} a = \frac{\sqrt{3}}{4} a^2

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Isosceles Triangle

Let the equal sides be a . Let the base be 2b . Then

1.       Perimeter = 2a+ 2b

2.       Height = \sqrt{a^2 - b^2}

3.       Area = \frac{1}{2} \times 2b \times \sqrt{a^2 - b^2} = b \sqrt{a^2 - b^2}

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Rectangle

Let the length = l and breadth = b . Then

1.       Perimeter = 2 (l+b)

2.       Area = lb

3.       Diagonal = \sqrt{l^2 + b^2}

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Square

Let the side of the square = a . Then

1.       Perimeter = 4a

2.       Area = a^2

3.       Diagonal = \sqrt{2} a

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Parallelogram

Let the two adjacent sides of the parallelogram be a and b

1.       Perimeter = 2 (a+b)

2.       Area = Base \times Height

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Rhombus

A parallelogram that has all the sides equal is called a rhombus. If d_1 and d_2 are the diagonals, then

1.       Side = \frac{1}{2} \sqrt{{d_1}^2 + {d_2}^2}

2.       Perimeter = 4 \times Side = 2\sqrt{{d_1}^2 + {d_2}^2}

3.       Area = \frac{1}{2} d_1 d_2

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Trapezium

A trapezium is a quadrilateral two of whose sides are parallel. A trapezium whose non-parallel sides are equal is known as an isosceles trapezium.

Let a and b be the parallel sides and h be the distance between the parallel sides. Then

1.       Area = \frac{1}{2} (a+b) \times h

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Quadrilateral

If h_1 and h_2 are the perpendicular distances from the diagonal AC of the quadrilateral ABCD from the vertices B and D respectively. Then,

1.       Area = \frac{1}{2} (AC)(h_1 + h_2)

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