Answer:
9. (DC)(BC) + 4(1/2)(BC)(VE): Surface Area of the Pyramid.
1. Point V: Vertex of the Pyramid.
6. Segment VO: Altitude of the Pyramid.
Step-by-step explanation:
Surface Area of the Pyramid
The surface area of a square-based pyramid consists of the area of its base and the combined areas of its 4 congruent triangular faces.
The base of the given pyramid is a square, so its area can be expressed as the product of its width (DC) and length (BC).
[tex]\textsf{Base area} = \sf (DC)(BC)[/tex]
The area of a triangle is half the product of its base and height.
The base of one triangular face is BC and the height is VE, so the area of one triangular face can be expressed as:
[tex]\textsf{Triangular face area} =\sf \dfrac{1}{2}(BC)(VE)[/tex]
Therefore, the total surface area of the pyramid is the base area plus the sum of the areas of its four triangular faces:
[tex]\textsf{Total surface area}=\sf (DC)(BC)+4\left(\dfrac{1}{2}\right)(BC)(VE)[/tex]
[tex]\hrulefill[/tex]
Vertex of the Pyramid
The vertex of a square-based pyramid is the highest point located directly above the center of the square base. It is the point where all the triangular faces meet.
Therefore, the vertex of the given pyramid is point V.
[tex]\hrulefill[/tex]
Altitude of the Pyramid
The altitude of a pyramid is the perpendicular distance from the vertex to the center of the base.
In the given pyramid, the vertex is point V and the center of the base is point O. Therefore, the altitude is segment VO.
