AMSCO'S Geometry. New York - Rye High School

452 The Geometry of Three DimensionsExercisesWriting About Mathematics1. Martin said that if the base of a regular pyramid is an equilateral triangle, then the foot ofthe altitude of the pyramid is the point at which the altitudes of the base intersect. Sarahsaid that it is the point at which the medians intersect. Who is correct? Justify your answer.2. Are the lateral faces of a pyramid always congruent triangles? Explain your answer.Developing SkillsIn 3–5, the information refers to a regular pyramid. Let e be the length of an edge of the base andh sbe the slant height. Find lateral area of each pyramid.3. The pyramid has a square base; e 12 cm, h s 10 cm4. The pyramid has a triangular base; e 8.0 ft, h s 10 ft5. The pyramid has a base that is a hexagon; e 48 cm, h s 32 cmIn 6–9, the information refers to a regular pyramid. Let e be the length of an edge of the base andh pbe the height of the pyramid. Find the volume of each pyramid.6. The area of the base is 144 square centimeters; h p 12 cm7. The area of the base is 27.6 square inches; h p 5.0 in.8. The pyramid has a square base; e 2 ft, h p 1.5 ft9. The pyramid has a square base; e 22 cm, h p 14 cm10. The volume of a pyramid is 576 cubic inches and the height of the pyramid is 18 inches. Findthe area of the base.Applying Skills11. A tetrahedron is a solid figure made up of four congruent equilateral triangles. Any one ofthe triangles can be considered to be the base and the other three to be the lateral sides of aregular pyramid. The length of a side of a triangle is 10.7 centimeters, the slant height is 9.27centimeters, and the height of the prism is 8.74 centimeters.a. Find the area of the base of the tetrahedron.b. Find the lateral area of the tetrahedron.c. Find the total surface area of the tetrahedron.d. Find the volume of the tetrahedron.12. When Connie camps, she uses a tent that is in the form of a regular pyramid with a squarebase. The length of an edge of the base is 9 feet and the height of the tent at its center is 8feet. Find the volume of the space enclosed by the tent.13. Prove that the lateral edges of a regular pyramid with a base that is an equilateral triangleare congruent.