Question

Find the lateral surface area of a triangular-based pyramid in which the area of a triangular face is 40cm².​

Answer 1

Answer:

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=1/2

Pl= 1/2 ×24×14=168 cm2

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

B=s 2=6 2=36 cm2

The general formula for the total surface area of a regular pyramid is TSA= 1/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= 1/2Pl=168 cm2

and area of the base is B=36 cm2

, therefore, the total surface area is:

TSA= 1/2Pl+B=168+36=204 cm2

Hence, lateral surface area of the pyramid is 168 cm2

and total surface area is 204 cm2

.

(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= 1/2

Pl= 1/2

×36×20=360 cm2

Now, the area of the base B= √3/4s2 with s=12 cm is:

B=√3/4s2=√3/4×12×12=36√3cm2

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

Since LSA= 1/2Pl=360 cm 2 and area of the base is B=36√3cm2 , therefore, the total surface area is:

TSA= 1/2Pl+B=360+36√3=36(10+√3) cm2

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

and total surface area is 36(10+√3)cm2

Hope this answer will be helpful for you ❤️