Teas 7 Area and Perimeter
Fundamental Geometric Shapes: Area
and Perimeter
This section outlines the formulas for calculating the area and perimeter of
several fundamental geometric shapes. Understanding these formulas is crucial for
various mathematical and practical applications.
1. Square
A square is a quadrilateral with four equal sides and four right angles.
Area (A): The area of a square is calculated by multiplying the length of one
side by itself. A=a×a=a2 where 'a' represents the length of a side.
Perimeter (P): The perimeter of a square is the total length of all its sides.
Since all sides are equal, it is calculated by adding the length of one side
four times. P=a+a+a+a=4a where 'a' represents the length of a side.
2. Rectangle
A rectangle is a quadrilateral with four right angles and opposite sides that are
equal in length.
Area (A): The area of a rectangle is found by multiplying its length by its
width. A=a×b where 'a' represents the length and 'b' represents the width.
Perimeter (P): The perimeter of a rectangle is the total length of all its
sides, which is twice the sum of its length and width. P=a+a+b+b=2(a+b)
where 'a' represents the length and 'b' represents the width.
3. Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides.
Area (A): The area of a parallelogram is calculated by multiplying the
length of its base by its height. The height is the perpendicular distance
, between the base and its opposite side. A=b×h where 'b' represents the base
and 'h' represents the height.
Perimeter (P): The perimeter of a parallelogram is the total length of all its
sides, which is twice the sum of the lengths of two adjacent sides.
P=a+a+b+b=2(a+b) where 'a' and 'b' represent the lengths of the adjacent
sides.
4. Trapezoid (or Trapezium)
A trapezoid (in the US) or trapezium (in the UK) is a quadrilateral with at least one
pair of parallel sides. These parallel sides are called the bases.
Area (A): The area of a trapezoid is calculated by multiplying half the sum
of the lengths of its parallel sides by its height. The height is the
perpendicular distance between the parallel sides. A=2(a+b)×h where 'a' and
'b' represent the lengths of the parallel sides (bases), and 'h' represents the
height.
Perimeter (P): The perimeter of a trapezoid is the sum of the lengths of all
its four sides. P=a+b+c+d where 'a' and 'b' are the lengths of the parallel
sides, and 'c' and 'd' are the lengths of the non-parallel sides.
5. Triangle
A triangle is a polygon with three sides and three angles.
Area (A): The area of a triangle is calculated by multiplying half the length
of its base by its height. The height is the perpendicular distance from a
vertex to the opposite side (the base). A=2b×h where 'b' represents the base
and 'h' represents the height.
Perimeter (P): The perimeter of a triangle is the sum of the lengths of its
three sides. P=a+b+c where 'a', 'b', and 'c' represent the lengths of the three
sides.
6. Right Triangle
A right triangle is a triangle with one angle equal to 90 degrees (a right angle). The
two sides that form the right angle are called the legs, and the side opposite the
right angle is called the hypotenuse.
Fundamental Geometric Shapes: Area
and Perimeter
This section outlines the formulas for calculating the area and perimeter of
several fundamental geometric shapes. Understanding these formulas is crucial for
various mathematical and practical applications.
1. Square
A square is a quadrilateral with four equal sides and four right angles.
Area (A): The area of a square is calculated by multiplying the length of one
side by itself. A=a×a=a2 where 'a' represents the length of a side.
Perimeter (P): The perimeter of a square is the total length of all its sides.
Since all sides are equal, it is calculated by adding the length of one side
four times. P=a+a+a+a=4a where 'a' represents the length of a side.
2. Rectangle
A rectangle is a quadrilateral with four right angles and opposite sides that are
equal in length.
Area (A): The area of a rectangle is found by multiplying its length by its
width. A=a×b where 'a' represents the length and 'b' represents the width.
Perimeter (P): The perimeter of a rectangle is the total length of all its
sides, which is twice the sum of its length and width. P=a+a+b+b=2(a+b)
where 'a' represents the length and 'b' represents the width.
3. Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides.
Area (A): The area of a parallelogram is calculated by multiplying the
length of its base by its height. The height is the perpendicular distance
, between the base and its opposite side. A=b×h where 'b' represents the base
and 'h' represents the height.
Perimeter (P): The perimeter of a parallelogram is the total length of all its
sides, which is twice the sum of the lengths of two adjacent sides.
P=a+a+b+b=2(a+b) where 'a' and 'b' represent the lengths of the adjacent
sides.
4. Trapezoid (or Trapezium)
A trapezoid (in the US) or trapezium (in the UK) is a quadrilateral with at least one
pair of parallel sides. These parallel sides are called the bases.
Area (A): The area of a trapezoid is calculated by multiplying half the sum
of the lengths of its parallel sides by its height. The height is the
perpendicular distance between the parallel sides. A=2(a+b)×h where 'a' and
'b' represent the lengths of the parallel sides (bases), and 'h' represents the
height.
Perimeter (P): The perimeter of a trapezoid is the sum of the lengths of all
its four sides. P=a+b+c+d where 'a' and 'b' are the lengths of the parallel
sides, and 'c' and 'd' are the lengths of the non-parallel sides.
5. Triangle
A triangle is a polygon with three sides and three angles.
Area (A): The area of a triangle is calculated by multiplying half the length
of its base by its height. The height is the perpendicular distance from a
vertex to the opposite side (the base). A=2b×h where 'b' represents the base
and 'h' represents the height.
Perimeter (P): The perimeter of a triangle is the sum of the lengths of its
three sides. P=a+b+c where 'a', 'b', and 'c' represent the lengths of the three
sides.
6. Right Triangle
A right triangle is a triangle with one angle equal to 90 degrees (a right angle). The
two sides that form the right angle are called the legs, and the side opposite the
right angle is called the hypotenuse.
