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.

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.