Question

26
The perimeter of the base of a square pyramid is 96cm and its height is 16cm.
(a) What is the length of a base edge?
(b) What is the slant height?
(c) Find the lateral surface area?​

Answer 1

Answer :

• The length of the base is 24cm
• Slant height is 20cm
• Lateral surface area is 960cm²

Given:

• The perimeter of the base of a square pyramid is 96cm
• Height is 16cm

To find :

• The length of a base edge
• The slant height
• The lateral surface area

Solution :

(a) What is the length of a base edge ?

Given that ,

• Perimeter of the base of a square is 96cm so,

As we know that,

• Perimeter of square = 4 × a

⇢ 4 × a = 96

⇢ a = 96/4

⇢ a = 24cm

The length of the base edge is 24cm

(b) What is the slant height ?

Given that ,

• base is 24cm
• Height is 16cm

As we know that,

Let the slant height be l

• Slant height = √ (base/2)² + h²

where , base is 24cm and height is 16cm

⇢ √ (24/2)² + 16²

⇢ √12² + 16²

⇢ √400

⇢ 20cm

Slant height is 20cm

(c) Find the lateral surface area :

⇢ 2al

where , a is base 24cm and l is slant height 20cm

⇢ 2 × 24 × 20

⇢ 960 cm²

Lateral surface area is 960cm²

Hence ,

• The length of the base edge is 24cm
• Slant height is 20cm
• Lateral surface area is 960cm²

Answer 2

Answer:

• The length of a base edge = 24 cm
• The Slant height = 20 cm
• The lateral surface area = 960 cm²

Step-by-step explanation:

Given that:

• The perimeter of the base of a square pyramid is 96 cm.
• Height of pyramid is 16 cm.

To Find:

(a) What is the length of a base edge?

(b) What is the slant height?

(c) Find the lateral surface area?

Formula used:

• Perimeter of a square = 4 × a
• Slant height of a square pyramid = h² + (1/4) a²
• Lateral surface area of square pyramid = a√(a² + 4h²)

Finding the length of a base edge:

• Perimeter of a square = 4 × a

⇒ 96 cm = 4 × a

⇒ a = (96 cm)/4

⇒ a = 24 cm

∴ Length of a base edge = 24 cm

Finding the slant height:

• Slant height = √{h² + (1/4) a²}

⇒ Slant height = √{(16)² + (1/4) × (24)²} cm

⇒ Slant height = √{256 + (1/4) × 576} cm

⇒ Slant height = √{256 + 144} cm

⇒ Slant height = √400 cm

⇒ Slant height = 20 cm

Finding the lateral surface area:

• Lateral surface area = a√(a² + 4h²)

⇒ Lateral surface area = 24√(24² + 4 × 16²) cm²

⇒ Lateral surface area = 24√(576 + 4 × 256) cm²

⇒ Lateral surface area = 24√(576 + 1024) cm²

⇒ Lateral surface area = 24√(1600) cm²

⇒ Lateral surface area = 24 × 40 cm²

⇒ Lateral surface area = 960 cm²