two similar pyramids have heights 9 and 12, Find the ratios of the base areas, lateral areas, total areas, and volumes.

Ratio of the total surface area = Ratio of the lateral areas = ratio of the base area = 9 : 16

Ratio of the volumes = 27 : 64

Step-by-step explanation:

Two similar pyramids have the heights 9 units and 12 units respectively.

Ratio of their heights are = =

By the property of similar figures,

"If the two figures are similar, their corresponding sides will be proportional".

Therefore, all the dimensions of these similar pyramids will be in the same ratio.

Therefore, ratio of their total surface areas = ratio of lateral areas = ratio of the base area = =

Similarly, ratio of their volumes = =

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)