# Area

In geometry, area is the space occupied by particular object or shape. The different shapes are having different areas. In our day to day life we come across many conditions like building construction, cloth stitching, in colouring also in which we want to know approximate areas of objects so that we can easily solve this type of problems.

The two dimensional object has area while the three dimensional object has surface area.

The area and surface area are measured in square units like meter square, feet square etc.

For example:

• If we draw a circle on paper then it is 2D object, then the area or space of paper occupied by that circle is the area of circle.
• But, if we have some gift which is enclosed in a box and we have to wrap it by paper. Now in this case we don’t want to know area because the box is 3D object. Hence, we want know the surface area of that box so that we can wrap it by paper properly.
• This is the difference between area and surface area.

Following are the some 2D -geometrical shapes and their formulae for area:

### 1) Rectangle:

• The rectangle is the quadrilateral in which opposite sides are equal and has 4 right angles at its four corners.
• Here we have to find the area of rectangle then we have to know its length and breadth also.
• If a is the length and b is the breadth of rectangle then its area is given by,
• area of rectangle =2* length*breadth = 2* (a * b)

### 2.) Square:

• Square is the rectangle whose all sides are equal in length.
• To find the area of square we have to know the one side length of square.
• If a is the length of side of square then its area is given by,
• area of square = square of side = a2

### 3.) Circle:

• Circle is the locus of points which are at a fixed distance from the centre point called as centre of circle.
• To find the area of circle we have to know only the radius of the circle.
• If r is the radius of circle then its area is given by,
• Area of circle = π* r2

### 4.) Semicircle:

• The semicircle means the half circle.
• If r is the radius of circle then the area of semicircle is given by,
• Area of semicircle= ½ (π*r2)

### 5.) Triangle:

• Triangle is the geometrical shape having three sides and three angles as shown in figure.
• To find its area we have to know the base and height of the triangle. Here in triangle ABC, BC is the base and AD is the height, then area of triangle is given by
• Area of triangle = ½ * base* height

### 6.) Equilateral triangle:

• Equilateral triangle is the triangle whose all three sides are equal and each internal angle measures as 600.
• To find the area of equilateral triangle we have to know only the length of one side of equilateral triangle.
• If a is the length of one side of equilateral triangle then its area is given by,
• Area of equilateral triangle = √3/4 * a2

### 7.) Isosceles triangle:

• Isosceles triangle is the triangle whose two sides are equal in length and third is different from them.
• And also the internal angles opposite to the equal sides are equal.
• To find the area of isosceles triangle we have to know the base and height of the triangle.
• If h is the height of equal sides and b is the base then the area of isosceles triangle is given by,
• Area of isosceles triangle = ½ * base*height = ½*b*h

For right angled isosceles triangle:

Then area of right angled isosceles triangle = ½ *base * height = ½ *a*a= ½*a2

### 8.) Parallelogram:

• Parallelogram is the quadrilateral with opposite sides are parallel and equal.
• The opposite angles in parallelogram are also equal and the adjacent angles sums to form the 1800.
• Here in parallelogram ABCD, AB ‖ DC, AD ‖ BC and AB=DC, AD=BC.
• Also, <D = <B, <A = <C and <A + <B = 1800, <D + <C = 1800.
• And the diagonals of parallelogram bisects each other.
• If AE is the height of the parallelogram and DC is the base then its area is given by
• Area  of parallelogram = base*height= DC*AE

### 9.) Rhombus:

• Rhombus is the special type of parallelogram in which all sides are equal in length.
• If d1 and d2 are the diagonals of rhombus then the area of rhombus is given by
• Area of rhombus = ½ * d1 * d2

### 10.) Trapezoid:

• Trapezoid is the quadrilateral with at least one pair of sides is parallel.
• And all sides are different in length of trapezoid.
• Here, AB and DC are the parallel sides of trapezoid then its area is given by,
• Area of trapezoid = ½ *(sum of parallel sides)

### 11) Regular hexagon:

• The hexagon is the polygon with 6 sides. But if the hexagon is the regular hexagon which is having all sides equal in length.
• If a is the length of one side of regular hexagon then its area is given by,
• Area of regular hexagon = 3√3/2* a2

### 12) Regular pentagon:

• Regular pentagon is the polygon with 5 sides and all these five sides are equal in length.
• If s is the length of one side of regular pentagon then its area is given by,
• Area of regular pentagon = 5/2 * s* a

Following are the some three dimensional geometrical shapes with their surface areas:

### 1.) Cube:

• Cube is the three dimensional object as shown in figure which is special cuboid having length, breadth and height and all are equal for cube and having 6 faces.
• Let a be the side of cube then the surface area of cube is given by,
• Surface area of cube = 6*a2

### 2) Cuboid:

• The cuboid is the three dimensional figure as shown in figure having six faces and having length, breadth and height also which are all different in length also.
• If l is length, b is the breadth and h is the height of the cuboid then its surface area is given by,
• Surface area of cuboid = 2(l*b + b*h + l*h)

### 3) Cylinder:

• It is the solid bounded by a cylindrical surface and two parallel planes.
• If r is the radius of circular base of the cylinder and h is the height of the cylinder then its surface area is given by,
• Surface area of cylinder = perimeter of circular base*(radius + height) = 2πr*(r + h)

### 4.) Cone:

• The cone is the three dimensional figure having flat surface as well as curved surface pointed towards the top as shown in figure.
• If r is the radius of circular base of cone, l is the slant height of the cone and h if the height of the cone then the surface area of cone is given by,
• Surface area of cone = π*r(l + r)

### 5) Sphere:

• Sphere is three dimensional geometrical figure having surface area and volume like a ball.
• If r is the radius of sphere then the surface area of sphere is given by,
• Surface area of sphere = 4*π*r2
• And the surface area of hemisphere is given by,
• Surface area of hemisphere = 3* π*r2

Updated: July 9, 2021 — 11:28 pm