I need the answer asap
Answers
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
.
Surface area:
The points A and B are the mid-points of WX and XY respectively.
For triangle VWX, the surface area is half the base(66) multiplied by the slant height VA of 56.
For triangle VXY, the surface area is half the base(32) times the slant height of 63.
Add and double the two areas to get the total slant areas, add to the area of the base, a rectangle 66x32, to get the total surface area.
Height of Pyramid:
Drop a perpendicular from V to the centre of the base at point D. Then VAD and VBD are right triangles.
VA=56, AD=XY/2=16, VD=√2880 by Pythagoras theorem.
Similarly,
VB=63, BD=WX/2=33, and again, VD=√(63²-33²)=√2880.
Therefore height of pyramid=√2880.
Volume:
Volume of a pyramid is the area of the base multiplied by (1/3) of the height.
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬