A regular square pyramid with the height of 2 meters and a base edge of 2 meters.
To find the surface area of the composite solid we will find surfaces areas from the prism and from the pyramid, then add them together.
Surface Area of the Pyramid
Only the lateral area of the pyramid is part of the surface area of the composite solid. The lateral area of a right pyramid is given by the following formula.
L.A.=1/2Pl
Here, P is the perimeter of the base and l is the slant height of the pyramid. Since the base is a square with an edge of 2 meters, its perimeter is P=4* 2=8 meters. Now, let's find the slant height, l.
Segment AB is half of the base edge of the pyramid. Therefore, AB= 22=1 meter. Now, let's use the Pythagorean Theorem for right triangle △ ABC.
The surface area from the part of the pyramid is about 8.96 square meters.
Surface Area of the Prism
The lateral area of the prism and one base area is part of the surface area of the given composite solid. The lateral area of a right prism is L.A.=Ph, where P is the perimeter of the base and h is the height of the prism.
L.A.=Ph
Since the base is a square with a base edge of 2 meters, its perimeter is P=4* 2=8 square meters. Therefore, L.A.=8* 4=32 m^2. Since the base is a square with base edge 2 m, its area is B=2^2=4 m^2. Therefore, the part of the surface area of the composite solid from the prism is 32+4=36 square meters.
Surface Area of Composite Solid
Now, let's add the partial surface areas and round it to the nearest whole number to find the answer.
S.A. & =8.96+36
& = 44.96 ≈ 45
This tells us that the surface area of the given solid is about 45 square meters.
