Which statements are true about a rectangular pyramid with a height of 15 inches and a base with the dimensions of 12 inches and 9 inches? Check all that apply.1.The area of the base of the pyramid, B, is 36 in32.The area of the base of the pyramid, B, is 108 in33.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid.4.The volume of this pyramid is 540in 35.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid.

Answer:2.The area of the base of the pyramid, B, is 108 in34.The volume of this pyramid is 540in 35.A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid.Step-by-step explanation:Verify each statementPart 1) The area of the base of the pyramid, B, is 36 in3The statement is falseBecauseThe area of the base of the pyramid is equal to[tex]B=(12)(9)=108\ in^{2}[/tex]Part 2) The area of the base of the pyramid, B, is 108 in3The statement is truesee the Part 1)Part 3) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have the same volume as this pyramid.The statement is falseBecauseThe volume of the pyramid is equal to[tex]V=\frac{1}{3}BH[/tex]substitute[tex]V=\frac{1}{3}(108)(15)=540\ in^{3}[/tex]The volume of the rectangular prism is equal to[tex]V=BH[/tex]substitute[tex]V=(108)(15)=1,620\ in^{3}[/tex]Compare[tex]540\ in^{3}\neq 1,620\ in^{3}[/tex]Part 4) The volume of this pyramid is 540in 3The statement is truesee the part 3)Part 5) A rectangular prism with the dimensions of 9 in. by 12 in. by 15 in. will have 3 times volume of this pyramid. The statement is trueBecausewe haveVolume of the pyramid ------> [tex]540\ in^{3}[/tex]Volume of the rectangular prism -----> [tex]1,620\ in^{3}[/tex]Divide the volume of rectangular prism by the volume of the pyramid [tex]1,620\ in^{3}/540\ in^{3}=3[/tex]thereforeThe volume of the rectangular prism is 3 times greater than the volume of the pyramid