Question

The uppermost part of each of following solid is a sq. Based pyramid.find T.S.A of Solids

Answer 1

Step-by-step explanation:

$\huge\tt\underline\red{QuestioN}:-$

Find the lateral and total surface area of the following pyramids.

(a) Square-based pyramid with base 6cm and slant height 14cm;

(b) Triangular-based pyramid with base 12cm and slant height 20cm

$\huge \tt\underline{\text{A} \blue{N} \orange{S} \pink{W} \green{E} \red{R}} :) :)$

(a) The perimeter of the base is P=4s, since it is a square, therefore,

P=4×6=24 cm

The general formula for the lateral surface area of a regular pyramid is LSA = 1/2

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=24 cm and the slant height is l=14 cm, therefore, the lateral surface area is:

$LSA= \frac{1}{2} Pl= \frac{1}{2} ×24×14=168 c {m}^{2}$

Now, the area of the base B=s^2 with s=6 cm is:

Base =s^2 =6^2 =36 cm^2

The general formula for the total surface area of a regular pyramid is TSA= 1/2 Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA= 1/2 Pl=168 cm^2 and area of the base is B=36 cm^2, therefore, the total surface area is:

$TSA= \frac{1}{2} Pl+B=168+36=204 c {m}^{2}$

Hence, lateral surface area of the pyramid is 168 cm^2 and total surface area is 204 cm^2.

b) The perimeter of the base is P=4s, since it is a triangle, therefore,

P=3×12=36 cm

The general formula for the lateral surface area of a regular pyramid is LSA= 1/2 Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=36 cm and the slant height is l=20 cm, therefore, the lateral surface area is:

$LSA= \frac{1}{2} Pl= \frac{1}{2} ×36×20=360 c {m}^{2}$

$\tt{Now, \: the \: area \: of \: the \: base B= \frac{ \sqrt{3} }{4} {s}^{2}  with s=12 cm \: is:}$

$b = \frac{ \sqrt{3} }{4} {s}^{2} = \frac{ \sqrt{3} }{4} \times 12 \times 12 \\ = 36 \sqrt{3 } {cm}^{3}$

The general formula for the total surface area of a regular pyramid is TSA= 1/2 Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA= 1/2 Pl=360 cm^2 and area of the base is B=36 3 cm^2, therefore, the total surface area is:

$TSA= \frac{1}{2} Pl+B=360+36 \sqrt{3} \\ =36(10+3) c {m}^{2}$

Hence, lateral surface area of the pyramid is 360 cm^2 and total surface area is

$\tt \blue{area = 36(10+3) c {m}^{2}}$

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