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A shape can be defined as a form or a figure enclosed by a boundary. We can see various types of shapes around us such as the rectangular shape of a book or the circular shape of the wheels of a bicycle. Area is defined as the measure of the space occupied by any shape. Here we will learn about different types of shapes and the methods to determine their area....Read MoreRead Less

Shapes, or geometric shapes are figures with outer boundaries that are created by combining curves, points, and lines. A shape can be an open shape or a closed shape.

As you can see, in the first image, the line segment of the shape does not meet, whereas in the second image, the shape is a closed figure with connected curves.

Closed shapes can be further classified into two types:

- Two-dimensional shapes
- Three-dimensional shapes

Two-dimensional or 2D shapes are flat plane figures with two dimensions — **length** and **width**. There is no thickness in 2D shapes. Some examples of two-dimensional shapes are circles, triangles, squares, rectangles, and pentagons.

Three-dimensional or 3D shapes are solid figures or objects that have three dimensions — **length**, **width**, and **height**. Some examples of three-dimensional shapes are cubes, rectangular prisms, spheres, cones, and cylinders.

Area is defined as the measure of space within the boundary of a shape. Area is usually represented by the number of square units, such as square centimeters, square feet, square inches, and so on.

The area of any 2D shape is given by the measure of space enclosed within its boundary.

The formula used to calculate the area of a 2D shape depends upon the type of 2D shape.

Area of square

**Area = Side x Side**

** = s x s**, where s is the length of the side of the square.

**Area of a rectangle**

**Area = Length x Width**

** = l x w**, where l is the length and w is the width of the rectangle.

**Area of a triangle**

**Area = \( \frac{1}{2}\times b \times h \)**, where b is the base and h is the height of the triangle.

**Area of a circle**

**Area = \( \pi \times r^2 \)**, where r is the radius of the circle.

**Area of a parallelogram**

**Area = b x h**, where b is the base and h is the vertical height.

**Area of a trapezoid**

**Area = \( \frac{1}{2}(a+b)\times h \)**, where a and b are the lengths of the parallel sides and h is the height or the perpendicular distance between parallel sides.

A 3D shape consists of multiple surfaces, so the area of a 3D shape is the sum of the areas of these surfaces. Hence, the area in 3D shapes is known as the **surface area**.

The formula used to determine the area of a 3D shape depends upon the type of 3D shape.

**Surface area of cube**

**Surface area** = 6a\( ^2 \), where a is the length of the edge of the cube.

**Surface area of a cuboid or rectangular prism**

**Surface area = 2(lh + wh + lw)**, where l is the length, h is the height, and w is the width of the cuboid.

**Surface area of a cylinder**

**Surface area = 2πr(r + h)**, where r is the radius of the circular base and h is the height of the cylinder.

**Surface area of a sphere**

**Surface area = 4πr****\( ^2 \)**, where r is the radius of the sphere.

**Surface area of a cone**

**Surface area = πr(r + l)**, where r is the radius of the circular base and l is the slant height of the cone.

**Example 1: Find the area of a circular garden whose radius is 14 m.**

**Solution:** Here, the **radius** of the circular garden is 14 m.

The formula for the area of a circle is given by \( \pi r^2 \) and \( \pi \) is \( \frac{22}{7} \).

So, Area \( =\pi r^2 \)

\( ~~~~~~~~~~~~~~=\frac{22}{7}\times 14\times 14 \) [Substitute values]

\( ~~~~~~~~~~~~~~=616 \) sq.m. [Simplify]

Hence, the area of the circular garden is 616 sq.m.

**Example 2: Find the surface area of a cone if the radius is 6 cm and the slant height is 4 cm.**

**Solution:** Here, the radius is 6 cm and the slant height is 4 cm.

As per the formula, the surface area of a cone \( =\pi r(r+l) \)

Surface area \( =\pi \times 6(6+4) \)

\( ~~~~~~~~~~~~~~~~~~~~~=\frac{22}{7}\times 6\times 10 \) [Substitute values]

\( ~~~~~~~~~~~~~~~~~~~~~=188.57 \) cm\( ^2 \) [Simplify]

Hence, the surface area of the cone is 188.57 cm\( ^2 \).

**Example 3: Alice bought a cuboid-shaped aquarium. Its dimensions are 6 cm, 4 cm, and 3 cm. What is the surface area of the aquarium?**

**Solution:** Here, the length of the aquarium is 6 cm, the height is 4 cm, and the width is 3 cm. So, the surface area of the aquarium is given by \( 2(lh + wh + lw) \).

Surface area \( =2(lh + wh + lw) \)

\( ~~~~~~~~~~~~~~~~~~~~~= 2 (6 \times 4 + 3 \times 4 + 6 \times 3) \) [Substitute values]

\( ~~~~~~~~~~~~~~~~~~~~~= 2 (24 + 12 + 18) \) [Simplify]

\( ~~~~~~~~~~~~~~~~~~~~~= 2 \times 54 \) [Simplify further]

\( ~~~~~~~~~~~~~~~~~~~~~= 108 \) cm \( ^2 \) [Multiply]

The surface area of the aquarium is 108 cm\( ^2 \).

Frequently Asked Questions

A 2D shape is drawn in two dimensions — length and width. In comparison a 3D shape is drawn using three dimensions — length, width, and height or thickness.

A solid shape is a three-dimensional object that has three dimensions.

A polygon is a closed two-dimensional shape bounded by straight lines. Examples: triangle, square, rhombus, trapezium, pentagon, and so on.

A quadrilateral is a type of polygon with exactly four sides. Examples: square, rectangle, parallelogram, and so on.

Area is the measure of space occupied by a flat surface in a 2D plane, whereas surface area is the sum of the measures of the area of the surfaces exposed in a 3D shape.

If you see that your child is struggling with a particular concept or operation that you thought they had mastered, a math worksheet is a great way to review previously practiced skills.