Look at the rectangular pyramid below.
What is the lateral surface area in square inches, of the figures formed by the net?
A.24 in224 in2
B.47 in247 in2
C.71 in271 in2
D.94 in2
Answers
Answer:
(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=
2
1
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=
2
1
Pl=
2
1
×24×14=168 cm
2
Now, the area of the base B=s
2
with s=6 cm is:
B=s
2
=6
2
=36 cm
2
The general formula for the total surface area of a regular pyramid is TSA=
2
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=
2
1
Pl=168 cm
2
and area of the base is B=36 cm
2
, therefore, the total surface area is:
TSA=
2
1
Pl+B=168+36=204 cm
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=
2
1
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=
2
1
Pl=
2
1
×36×20=360 cm
2
Now, the area of the base B=
4
3
s
2
with s=12 cm is:
B=
4
3
s
2
=
4
3
×12×12=36
3
cm
2
The general formula for the total surface area of a regular pyramid is TSA=
2
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=
2
1
Pl=360 cm
2
and area of the base is B=36
3
cm
2
, therefore, the total surface area is:
TSA=
2
1
Pl+B=360+36
3
=36(10+
3
) cm
2
Hence, lateral surface area of the pyramid is 360 cm
2
and total surface area is 36(10+
3
) cm
2
.