Simon Builds this podium on a platform.
What is the combined volume of the podium and the platform?
(Help me!) I just need help understanding how to do this type of thing! :)

  64 cubic feet

Step-by-step explanation:

You do this type of thing by dividing the figure into parts whose volumes are easy to figure.

This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere. The volume is the area of the front face times that depth.

1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is ...

  (2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft²

so, the total volume is ...

  V = frontal area × depth = (32 ft²)(2 ft) = 64 ft³

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2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom. The frontal area calculated this way is ...

  (2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft² . . . . . as before

Again, the total volume is (32 ft²)(2 ft) = 64 ft³.

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3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is ...

  (6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above

Again, the total volume is (32 ft²)(2 ft) = 64 ft³.

x = 20 ; y= 10√3

Step-by-step explanation:

30, 60 , 90 triangle ratio is

Side opposite to 30 is a

a = AC = 10

Side opposite to 60 is a

AB = a = 10√3

Side opposite to 90 is  2a

BC = 2a = 2* 10 = 20