+84 1)ABCDEFGH is a rectangular prism with AB = 3, BC = 4 and AE = 5. Find the area of quadrilateral ACGE.
Picture: https://latex.artofproblemsolving.com/7/6/2/762db8d3630f22f95d36a108ac78a0f9ccd1cfc7.png
2)ABCDE is a right square pyramid with DE = 6 and AC = 3sqrt5. Find the total surface area of the pyramid.
Picture: https://latex.artofproblemsolving.com/7/7/8/778f246107c25df76fceca5030d60d931cdc3ffc.png
3)What is the total surface area of this prism?
Picture: https://latex.artofproblemsolving.com/5/6/0/560705e80bff3c49125009a1363cbbbec9c1a7df.png
4)A right pyramid has a regular hexagon as a base. The slant height is 20, and the perimeter of its base is 10. What is the lateral surface area of the pyramid?
5)A rectangular prism has dimensions 8, 12, and 16. What is the length of its longest face diagonal?
6)Two cubes of volumes 8 and 27 are glued together at their faces to form a solid with the smallest possible surface area. What is the surface area of the resulting solid?
7)A pyramid and a prism share the same base. The prism has 99 edges. How many faces does the pyramid have?
8)Three face diagonals of a rectangular prism have lengths sqrt19, sqrt23 and sqrt30. Find the length of its space diagonal.
Picture: https://latex.artofproblemsolving.com/d/5/9/d5922081d2e017c395df8874c6d4b57bbc93437f.png
9)Each of the eight edges of a regular square pyramid has length 2. The volume of the pyramid is V. Find V^2.
10)Let ABCDE be a pyramid, where the base ABCD is a square of side length 10. The total surface area of pyramid ABCDE (including all five faces) is 260.
Let M, N, P, and Q be the midpoints of AE, BE, CE, and DE, respectively. Find the total surface area of frustum ABCDMNPQ.
Picture:https://latex.artofproblemsolving.com/8/e/6/8e6bd9fb08db9450dd766f2ab3bce921e01e8f21.png
11)Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.
Picture: https://latex.artofproblemsolving.com/0/a/3/0a3404805162de58ee7c86ac6b0e5d23327c0026.png
+12531 1)ABCDEFGH is a rectangular prism with AB = 3, BC = 4 and AE = 5. Find the area of quadrilateral ACGE.
+12531 2)ABCDE is a right square pyramid with DE = 6 and AC = 3sqrt5. Find the total surface area of the pyramid.
+12531
4)A right pyramid has a regular hexagon as a base. The slant height is 20, and the perimeter of its base is 10. What is the lateral surface area of the pyramid?
+12531
5)A rectangular prism has dimensions 8, 12, and 16. What is the length of its longest face diagonal?
+12531 6)Two cubes of volumes 8 and 27 are glued together at their faces to form a solid with the smallest possible surface area. What is the surface area of the resulting solid?
+12531 7)A pyramid and a prism share the same base. The prism has 99 edges. How many faces does the pyramid have?
99 : 3 = 33
33 *2 = 66
+12531
8)Three face diagonals of a rectangular prism have lengths sqrt19, sqrt23 and sqrt30. Find the length of its space diagonal.
+12531 9)Each of the eight edges of a regular square pyramid has length 2. The volume of the pyramid is V. Find V^2.
+12531
10)Let ABCDE be a pyramid, where the base ABCD is a square of side length 10. The total surface area of pyramid ABCDE (including all five faces) is 260.
Let M, N, P, and Q be the midpoints of AE, BE, CE, and DE, respectively. Find the total surface area of frustum ABCDMNPQ.
