Question

Base perimeter of a square pyramid is 32cm and it's height is 15cm . What is it lateral surface area?

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

$\sf\underline{\purple{\:\:\:\: Given\:\:\:\:}}$

$\sf\bullet Base\: perimeter\:of\:square\:pyramid=32cm\\ \\ \sf\bullet Height\:of\: pyramid=15cm$

• Now we have to find the Lateral surface area of pyramid

$\boxed{\sf{Perimeter\:of\:square\:pyramid= 4\times side}}$

$\boxed{\sf{L.S.A\:of\:square\:pyramid= 2bh}}$

Now first the side of pyramid

$\sf:\implies 4\times side=32\\ \\ \sf:\implies side=\cancel{\dfrac{32}{4}}\\ \\ \sf:\implies side= 8cm$

• Base of pyramid is 8cm
• Now L.S.A

$\sf:\implies L.S.A=2\times 8\times 15\\ \\ \sf:\implies L.S.A= 16\times 15\\ \\ \sf:\implies L.S.A= 240cm{}^{2}$

$\boxed{\sf{L.S.A\:of\:pyramid=240cm{}^{2}}}$

Answer 2

Answer:

${\sf\red{\underline{\sf\pink{\boxed{\sf\green{Lateral\: surface \: area = 240\: {cm}^{2}}}}}}}$

Step-by-step explanation:

$\frak\green{Given:-}\begin{cases}\sf\red{Perimeter \: of \: square \: pyramid = 32 \: cm}\\\sf\orange{Height = 15\: cm }\\\sf\pink{LSA \: of \: pyramid = ?}\end{cases}$

Now we can find LSA in 2 methods.

Method 1:-

First we have to find side of pyramid meaning the base of pyramid.

We know that,

$\boxed{\boxed{\sf\pink{Perimeter \: of \: square = 4 \times Side}}}$

$\hookrightarrow\sf 32 = 4 \times base \\\\\hookrightarrow\sf Base =\cancel{\dfrac{32}{4}} \: cm \\\\\hookrightarrow{\boxed{\sf\red{Base = 8 \: cm}}}$

Now we know that,

$\boxed{\boxed{\sf\orange{LSA \: of \: square\: pyramid = 2bh}}}$

$\hookrightarrow\sf LSA = 2 \times 8 \times 15 \\\\\hookrightarrow\large{\boxed{\sf\pink{LSA = 240 \: {cm}^{2} }}}$

$\therefore\bold{LSA \: of \: square \: pyramid = 240 \: {cm}^{2} }$

$\rule{200}{1}$

Method 2:-

In this method we can easily find the LSA of square pyramid.

Given:-

• Perimeter of square pyramid=32 cm
• Height = 15 cm

To find:-

• LSA of square pyramid.

We know that,

$\boxed{\boxed{\sf\green{LSA = \dfrac{Base \: perimeter \times Slant \: height}{2} }}}$

$\sf \: \: *Substituting\: values :-$

$\hookrightarrow\sf LSA = \dfrac{32 \times 15}{2} \\\\\hookrightarrow\sf LSA =\cancel{ \dfrac{480}{2}} \\\\\hookrightarrow\large{\sf\green{\boxed{\sf\gray{LSA = 240 \: {cm}^{2} }}}}$

${\underline{\boxed{\therefore{\sf\blue{LSA \: of \: square \: pyramid = 240 \: {cm}^{2} }}}}}$