Examples on Surface Area of Rectangular Pyramid
Example 1. Determine the lateral surface area of a rectangular pyramid if the base length is 10 inches and the base width is 8 inches, and the height of the pyramid is 12 inches.
Solution:
Given data,
- Base length (l) = 16 inches
- Base width (w) = 12 inches
- Height of the pyramid (h) = 15 inches
We know that,
Lateral Surface Area of a Rectangular Pyramid = l√[h2 + (w/2)2] + w√[h2 + (l/2)2]
= 10 × √[122 + (8/2)2] + 8 × √[122 + (10/2)2]
= 10 × √(144 + 16) + 8 × √(144 + 25)
= 10 × √160 + 8 × √169
= 10 × 12.649 + 8 × 13
= 126.49 + 104 = 230.49 sq. in
Hence, the lateral surface area of the given rectangular pyramid is 230.49 sq. in.
Example 2. Find the surface area of a rectangular pyramid if the base length is 8 cm and the base width is 6 cm, and the height of the pyramid is 10 cm.
Solution:
Given data,
- Base length (l) = 8 cm
- Base width (w) = 6 cm
- Height of the pyramid (h) = 10 cm
We know that,
Total surface area of a rectangular pyramid = l√[h2 + (w/2)2] + w√[h2 + (l/2)2] + l × w
= (8 × √[102 + (6/2)2] + 6 × √[102 + (8/2)2] + 8 × 6
= 8 × √(100 + 9) + 6 × √(100 + 16) + 48
= 8 × √109 + 6 × √116 + 48
= 8 × 10.440 + 6 × 10.770 + 48
= 83.522 + 64.621 + 48 = 196.143 sq. cm
Hence, the surface area of the given rectangular pyramid is 196.143 sq. cm.
Example 3. Find the total surface area of a rectangular pyramid if the base length is 12 cm and the base width is 10 cm, and the height of the pyramid is 15 cm.
Solution:
Given data,
- Base length (l) = 12 cm
- Base width (w) = 10 cm
- Height of the pyramid (h) = 15 cm
We know that,
Total surface area of a rectangular pyramid = l√[h2 + (w/2)2] + w√[h2 + (l/2)2] + l × w
= (10 × √[152 + (12/2)2] + 12 × √[152 + (10/2)2] + 12 × 10
= 10 × √(225 + 36) + 12 × √(225 + 25) + 120
= 10 × √261 + 12 × √250 + 120
= 10 × 16.155 + 12 × 15.811 + 120
= 161.554 + 189.736 + 120 = 471.29 sq. cm
Hence, the surface area of the given rectangular pyramid is 471.29 sq. cm.
Example 4. Determine the lateral surface area of a rectangular pyramid if the base length is 8 m and the base width is 4 m, and the height of the pyramid is 9 m.
Solution:
Given data,
- Base length (l) = 8 m
- Base width (w) = 4 m
- Height of the pyramid (h) = 9 m
We know that,
Lateral surface area of a rectangular pyramid = l√[h2 + (w/2)2] + w√[h2 + (l/2)2]
= 8 × √[92 + (4/2)2] + 4 × √[92 + (8/2)2]
= 8 × √(81 + 4) + 4 × √(81 + 16)
= 8 × √85 + 4 × √97
= 8 × 9.219 + 4 × 9.849
= 73.756 + 39.395 = 113.151 sq. m
Hence, the lateral surface area of the given rectangular pyramid is 113.151 sq. m.
Example 5. Find the surface area of a rectangular pyramid if the base length is 20 inches and the base width is 16 inches, and the height of the pyramid is 25 inches.
Solution:
Given data,
- Base length (l) = 20 inches
- Base width (w) = 16 inches
- Height of the pyramid (h) = 25 inches
We know that,
Total surface area of a rectangular pyramid = l√[h2 + (w/2)2] + w√[h2 + (l/2)2] + l × w
= (20 × √[252 + (16/2)2] + 16 × √[252 + (20/2)2] + 20 × 16
= 20 × √(625 + 36) + 16 × √(625 + 100) + 320
= 20 × √689 + 16 × √250 + 320
= 20 × 26.249 + 16 × 26.925 + 320
= 524.976 + 430.813 + 320 = 1,275.789 sq. in
Hence, the surface area of the given rectangular pyramid is 1,275.789 sq. in.
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