# Surface Area of a pyramid formula

## Surface Area of a pyramid formula

A pyramid  with polygonal base and triangular faces equal to the number of sides in the base. In a pyramid, the triangular faces meet at a single point known as apex. The base of the pyramid is connected with the faces of the pyramid. Since, each and every triangular face will have different size and shape, we would need to find the area of each using the formula given.

The different types of pyramid are given as:

1. Square Pyramid
2. Triangular Pyramid
3. Pentagonal Pyramid
4. Hexagonal Pyramid

### Square Pyramid

$\large Surface\;area\;of\;a\;square\;pyramid=2bs+b^{2}$

### Triangular Pyramid

$\large Surface\;area\;of\;a\;triangular\;pyramid=\frac{1}{2}ab+\frac{3}{2}bs$

### Pentagonal Pyramid

$\large Surface\;area\;of\;a\;pentagonal\;pyramid=\frac{5}{2}ab+\frac{5}{2}bs$

### Hexagonal Pyramid

$\large Surface\;area\;of\;a\;hexagonal\;pyramid=3ab+3bs$

### Solved Example

Question: Find out the Surface area of the square pyramid with side 5 cm and base 4 cm

Solution

Surface area of a square pyramid = 2bs + b2
Here, using the formula

= 2 x 4 x 5 + 4= 40 + 16
= $\large 56\;cm^{2}$

 More topics in Surface Area of a Pyramid Formula Surface Area of a Square Pyramid Formula

#### Practise This Question

The number of turns in the coil of an ac­ generator is 5000 and the area of the coil is
0.25m2. The coil is rotated at the rate of 100 cycles/sec in a magnetic field of 0.2 W/m2. The peak value of the emf generated is nearly