Solved Problems on Rectangular Pyramid

Problem 1: Find the surface area of a rectangular pyramid with the following dimensions:

• Length of the base (L) = 6 units
• Width of the base (W) = 4 units
• Height of the pyramid (H) = 8 units

Solution:

To find the surface area (SA), we’ll use the formula:

SA = L × W + (1/2) × P × S

Calculate the perimeter of the base (P):

P = 2(l + w)

⇒ P = 2(6 + 4)

⇒ P = 2(10) = 20 units

Calculate the slant height (S) using the Pythagorean theorem:

S = √(l² + w² + h²)

⇒ S = √(6² + 4² + 8²)

⇒ S = √(36 + 16 + 64)

⇒ S = √116 ≈ 10.77 units

Now, substitute these values into the surface area formula:

Surface Area = 6 × 4 + (1/2) × 20 × 10.77

⇒ Surface Area = 24 + 107.7 ≈ 131.7 square units`

So, the surface area of the rectangular pyramid is approximately 131.7 square units. 

Problem 2: Calculate the volume of a rectangular pyramid with a base length of 5 cm, a base width of 3 cm, and a height of 7 cm.

Solution:

To calculate the volume (V), we’ll use the formula:

V = (1/3) × L × W × H

Substitute the given values into the formula:

V = (1/3) × 5 cm × 3 cm × 7 cm

⇒ V = (1/3) × 105 cm³

⇒ V = 35 cm³

So, the volume of the rectangular pyramid is 35 cubic centimetres.

Problem 3: Calculate the slant height (S) of a rectangular pyramid with a base length of 8 inches, a base width of 6 inches, and a height of 10 inches.

Solution:

To find the slant height (S), we can use the Pythagorean theorem:

S = √(L² + W² + H²)

Substitute the given values into the formula:

S = √(8² + 6² + 10²)

S = √(64 + 36 + 100)

S = √200 ≈ 14.14 inches

The slant height of the rectangular pyramid is approximately 14.14 inches.

Rectangular Pyramid is one of the many pyramid structures in Geometry. A pyramid is a three-dimensional structure that has a polygon as its base and triangular faces covering its sides, meeting at a common point known as the apex of the pyramid. In the case of a rectangular pyramid, the base is a rectangle, which is why it is called a rectangular pyramid, with four triangular faces connecting the sides of the rectangle to the apex.

A Rectangular Pyramid can be either right or oblique, depending on the alignment of the apex and the center of the base. If the apex aligns with the center of the base at a right angle, then it is a right rectangular pyramid; if not, then it is an oblique rectangular pyramid.

This article provides a well-rounded description of the geometric solid known as the Rectangular Pyramid, including its definition, shapes, and types. In addition to that, we will also discuss the formulas for surface area and volume for the Rectangular Pyramid.