Area :
The amount of space inside the boundary of a two- dimensional shape such as a triangle or circle.
Perimeter :
Perimeter is the distance around a two-dimensional shape such as square or rectangle or triangle.
A square is a four-sided polygon where the lengths of all the four sides will be equal and each vertex angle will be right angle or 90° ^{ }as shown below.
When the side length is given :
Area of a Square = a^{2}
When the length of the diagonal is given :
Area of a Square = 1/2 ⋅ d^{2}
Perimeter of a Square = 4a
A rectangle is a four-sided polygon where the lengths of opposite sides will be equal and each vertex angle will be 90° or right angle as shown below.
Area of a Rectangle = l ⋅ w
Perimeter of a Rectangle = 2(l + w)
An equilateral triangle is a three-sided polygon where the lengths of all the three sides will be equal and each vertex angle will be 60° as shown below.
Area of an Equilateral Triangle = √3/4 ⋅ a^{2}
Perimeter of an Equilateral Triangle = 3a
An scalene triangle is a three-sided polygon where the all the three sides will have unequal lengths and the measures of all the three angles will be different as shown below.
Area of a Scalene Triangle = √[s(s - a)(s - b)(s - c)]
where s = (a + b + c)/2
Perimeter of a Scalene Triangle = a + b + c
A quadrilateral is a four-sided polygon as shown below.
Area of a Quadrilateral = 1/2 ⋅ d ⋅ (h_{1} + h_{2})
Perimeter of a Quadrilateral = a + b + c + d
A parallelogram is a four-sided polygon where the opposite sides will be equal and parallel as shown below.
Area of a Parallelogram = b ⋅ h
Perimeter of a Parallelogram = 2(a + b)
A rhombus is a four-sided polygon where the lengths of all the four sides will be equal and opposite sides will be parallel as shown below.
Area of a Rhombus = 1/2 ⋅ d_{1} ⋅ d_{2}
Perimeter of a Rhombus = 4a
A trapezoid is a four-sided polygon which has a pair of opposite sides parallel as shown below.
Area of a Trapezoid = 1/2 ⋅ h ⋅ (a + b)
Perimeter of a Trapezoid = a + b + c + d
A circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center). The distance between the center and any point on the circumference is called radius (r).
Area of a Circle = πr^{2}
Perimeter of a Circle = 2πr
A semicircle is a half of a circle or of its circumference as shown below.
Area of a Semicircle = πr^{2}/2
Perimeter of a Semicircle = πr + 2r
A quadrant is a one-fourth of a circle.
Area of a Quadrant = πr^{2}/4
Perimeter of a Quadrant = πr/2 + 2r
A sector of a circle is a part of the interior of the circle enclosed by an arc and two radii.
Area of a Sector = θ/360° ⋅ πr^{2}
Length of the Arc AB = θ/360° ⋅ 2πr
Perimeter a Sector = (θ/360° ⋅ 2πr) + 2r
A regular polygon is a polygon that is equiangular (all interior angles are equal in measure) and equilateral (all sides have the same length).
Area = 1/2 ⋅ (Apothem x Perimeter)
Perimeter = No. of sides ⋅ Length of each side
Problem 1 :
If the length of each side of a square is 5 cm, find its perimeter.
Solution :
Perimeter of the square = 4 x length of each side
= 4 x 5
= 20 cm
Problem 2 :
If the length and width of a rectangle are 4.2 in. and 7 in. respectively. Find its area.
Solution :
Area of the rectangle = length x width
= 4.2 x 7
= 29.4 in.^{2}
Problem 3 :
The length of a rectangle is 3 more than twice the width. If the perimeter of the rectangle is 36 cm, find the length and width of the rectangle.
Solution :
Let x be the width of the rectangle.
Then, length of the rectangle :
= 2x + 3
Perimeter of the rectangle = 36 cm
2(length + width) = 36
2(2x + 3 + x) = 36
2(3x + 3) = 36
Divide both sides by 2.
3x + 3 = 18
Subtract 3 from both sides.
3x = 15
Divide both sides by 3.
x = 5
2x + 3 = 2(5) + 3
2x + 3 = 10 + 3
2x + 3 = 13
Length and width of the rectangle are 13 cm and 5 cm respectively.
Problem 4 :
Find the area of a circle whose radius is 7 cm. Use π = 3.14 and round your answer to the nearest tenth.
Solution :
Area of the circle = πr^{2}
= 3.14 x 7^{2}
= 3.14 x 49
= 153.9 cm^{2}
Problem 5 :
If the radius of a circle is 6.5 in., find its circumference. Use π = 3.14 and round your answer to the nearest tenth.
Solution :
Circumference of the circle = 2πr
= 2 x 3.14 x 6.5
= 40.82 in.
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