Question

Base perimeter of square pyramid 32 cm and height 15 cm. find it's lateral surface area.
give anwer with step​

Answer 1

Answer:

• LSA (Lateral surface area) of square pyramid is 240 cm².

Step-by-step explanation:

Given :

• Base perimeter of square pyramid = 32 cm.
• Height of square pyramid = 15 cm.

To Find :

• Lateral surface area of square pyramid.

Calculations :

Firstly let's calculate the base of the cylinder. For calculating the base, we will divide base perimeter (32 cm) by 4.

$: \implies \sf \dfrac{Base \: perimeter}{4}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$: \implies \sf \cancel \dfrac{32}{4}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$: \implies\boxed{ \underline {\sf 8 \: cm }}$

• Therefore, base of the cylinder is 8 cm.

$\dag$ According to the Question,

Now coming to the question, here we are asked to calculate the LSA (Lateral surface area) of square pyramid.

In order to calculate the LSA (Lateral surface area) we'll be using this formula,

Formula used :

• $\boxed{ \rm{ \gray{2 \times base \times height}}}$

Where,

• Base = 8 cm
• Height = 15 cm

$\dag$ Putting the values,

$: \implies \sf LSA = 2 \times 8 \times 15 \: cm$

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$: \implies \sf LSA = 16 \times 15 \: cm$

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$: \implies \boxed{\sf LSA = 240 \: cm^2} \pink{ \bigstar}$

Henceforth,

• LSA (Lateral surface area) of square pyramid is 240 cm².

Answer 2

$\huge\bf{Concept :}$

In this problem, we're asked to find the lateral or curved surface area of a square pyramid when we're given with the base perimeter and measure of the altitude.

Here, after finding base (from base perimeter), we can calculate the lateral surface area.

Let's solve the problem.

Given :-

• Base perimeter of the pyramid = 32 cm
• Altitude of the pyramid = 15 cm

To find :-

• Lateral/curved surface area of the square pyramid.

$\huge\bf{Answer :}$

☆ We'll calculate the base from the relationship between the base and the base perimeter of the square pyramid.

We know that,

Base = $\frac{base \: perimetre}{4}$

⇒ $\frac{32}{4}$ = 8 cm

Now, we've both height and the base.

∴ By applying the formula of lateral surface area of the square pyramid, we can get our answer.

We know that,

Lateral surface area of pyramid = $2 \times base \times height$

• Inserting the values of given height and base,

⇒ 2 × 8 × 15 = 16 × 15

⇒ 240 cm² ✔️

Therefore, the lateral surface area of the square pyramid is 240 cm².