Examples on Triangular Pyramid Formula

Example 1: Determine the volume of a triangular pyramid whose base area and height are 50 cm² and 12 cm, respectively.

Solution:

Given data,

• Area of the triangular base = 100 cm²
• Height of the pyramid = 12 cm

We know that,

Volume of a triangular pyramid (V) = 1/3 × Area of triangular base × Height

V = 1/3 × 50 × 12 = 200 cm³

Hence, the volume of the given triangular pyramid is 200 cm³.

Example 2: Find the total surface area of a regular triangular pyramid when the length of each edge is 8 inches.

Solution:

Given data,

• Length of each edge of a regular triangular pyramid (a) = 8 inches

We know that,

Total surface area of a regular triangular pyramid = √3a²

⇒ TSA = √3 × 8²

= 64√3 = 110.851 sq. in

Hence, the total surface area of a regular triangular pyramid is 110.851 sq. in.

Example 3: Determine the volume of a regular triangular pyramid when the length of the edge is 10 cm.

Solution:

Given data,

• Length of each edge of a regular triangular pyramid (a) = 10 cm

We know that,

Volume of a regular triangular pyramid = a³/6√2

⇒ V = (10)³/6√2

= 1000/6√2 = 117.85 cm³

Hence, the volume of a regular triangular pyramid is 117.85 cu. cm.

Example 4: Find the slant height of the triangular pyramid if its lateral surface area is 600 sq. in. and the perimeter of the base is 60 inches.

Solution:

Given data,

• Lateral surface area = 600 sq. in
• Perimeter of the base = 60 inches

We know that,

Lateral surface area = ½ × perimeter × slant height

600 = ½ × 60 × l

l = 600/30 = 20 inches

Hence, the slant height of the given pyramid is 20 inches.

Example 5: Determine the total surface area of a triangular pyramid whose base area is 28 sq. cm, the perimeter of the triangle is 18 cm, and the slant height of the pyramid is 20 cm.

Solution:

Given data,

• Area of Triangular Base = 28 cm²
• Slant height (l) = 20 cm
• Perimeter (P) = 18 cm

We know that,

Total surface area (TSA) of a triangular pyramid = ½ × perimeter × slant height + Base area

⇒ TSA = ½ × 18 × 20 + 28

= 180 + 28 = 208 sq. cm

Hence, the total surface area of the given pyramid is 208 sq. cm.

Volume of a triangular pyramid is found using the formula V = 1/3A.H. A triangular pyramid, also known as a tetrahedron, is a type of pyramid with a triangular base and three triangular faces that meet at a single point called the apex.

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