Surface Area of a Rectangular Pyramid
Surface area is defined as the total region occupied by the surfaces of a three-dimensional figure, and it is measured in terms of square units such as cm2, m2, in2, ft2, etc. A rectangular pyramid has two types of surface areas, i.e., the lateral surface area and the total surface area.
Lateral Surface Area of Rectangular Pyramid
The lateral surface area of a rectangular pyramid is equal to the sum of the areas of its four lateral faces (triangular faces). In a rectangular pyramid, the areas of the opposite triangular faces are the same. To find the surface area of a rectangular pyramid, we need to know the measures of the base length, base width, and slant height of the triangular face.
Lateral Surface Area of a Pyramid (LSA) = Sum of Areas of Lateral surfaces (triangles) of Pyramid
Slant height of length face of the pyramid = β[h2 + (w/2)2]
Slant height of width face of the pyramid = β[h2 + (l/2)2]
We know that,
Area of a Triangle = Β½ Γ base Γ height
Area of the triangle that has a length as the base = Β½ Γ l Γ {β[h2 + (l/2)2]}
Area of the triangle that has a width as the base = Β½ Γ w Γ {β[h2 + (w/2)2}
Now, LSA = Β½ Γ l Γ {β[h2 + (w/2)2]} + Β½ Γ w Γ {β[h2 + (l/2)2} + Β½ Γ l Γ {β[h2 + (w/2)2]} + Β½ Γ w Γ {β[h2 + (l/2)2}
= 2 Γ {Β½ Γ l Γβ[h2 + (w/2)2]} + 2 Γ {Β½ Γ w Γβ[h2 + (l/2)2]}
= lβ[h2 + (w/2)2] + wβ[h2 + (l/2)2]
Lateral Surface Area of Rectangular Pyramid = lβ[h2 + (w/2)2] + wβ[h2 + (l/2)2]
where,
- βlβ is the Base Length
- βwβ is the Base Width
- βhβ is the Height of Pyramid
Total Surface Area
Total surface area of a rectangular pyramid is equal to the sum of the areas of its four lateral faces (triangular faces) and the area of its rectangular base. To determine the total surface area of a rectangular pyramid, we need to find the area of its rectangular base and its lateral surface area, i.e., the sum of the areas of its four triangular faces.
Total surface area of a pyramid (TSA) = Lateral Surface Area of Pyramid + Area of Base
Area of rectangular base = l Γ w
So, TSA = lβ[h2 + (w/2)2] + wβ[h2 + (l/2)2] + l Γ w
TSA of a Rectangular Pyramid = lβ[h2 + (w/2)2] + wβ[h2 + (l/2)2] + l Γ w
where,
- βlβ is the Base Length
- βwβ is the Base Width
- βhβ is the Height of Pyramid
Area of a Rectangular Pyramid
Understanding the area of a rectangular pyramid is essential for students, educators, and professionals alike. A rectangular pyramid, also known as a rectangular-based pyramid, is a three-dimensional geometric shape with a rectangular base and four triangular faces that meet at a common point called the apex.
In this article, we will discuss the surface area of a rectangular pyramid in detail.
Table of Content
- What is a Rectangular Pyramid?
- Net of Rectangular Pyramid
- Surface Area of a Rectangular Pyramid
- How to Calculate the Surface Area of a Rectangular Pyramid?
- Examples on Surface Area of Rectangular Pyramid