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The trapezoid shown in the figure above represents a cross [#permalink]

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19 Dec 2012, 05:18

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The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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19 Dec 2012, 05:23

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The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

(A) 39 (B) 40 (C) 42 (D) 45 (E) 46.5

Attachment:

Trapezoid2.png [ 9.67 KiB | Viewed 10270 times ]

The formula for calculating the area of a trapezoid is \(Area=\frac{1}{2}(base_1+base_2)(height)=\frac{1}{2}(2+5)(height)\).

So, we need to find the height AC: \(AC=\sqrt{AB^2-BC^2}=\sqrt{13^2-5^2}=12\).

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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29 Aug 2013, 22:57

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Bunuel wrote:

The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

(A) 39 (B) 40 (C) 42 (D) 45 (E) 46.5

Attachment:

Trapezoid2.png

The formula for calculating the area of a trapezoid is \(Area=\frac{1}{2}(base_1+base_2)(height)=\frac{1}{2}(2+5)(height)\).

So, we need to find the height AC: \(AC=\sqrt{AB^2-BC^2}=\sqrt{13^2-5^2}=12\).

Therefore, \(Area=\frac{1}{2}(2+5)*12=42\).

Answer: C.

You could save yourself some calculation here if you knew the pythagorean triple 5-12-13. That would shave a few seconds off of the problem. _________________

Please don't forget to give kudos if you found someone's post helpful. Everyone likes kudos!

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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30 Aug 2013, 00:02

Well I don't know the formula for calculating the area of trapezoid. Also, I like to solve sums without using paper pen and with few basic formulae.

I first found out the base (the bottomline in the question figure) using pythogoras triplet (5-12-13). Then I imagined the figure as right-angled triangle sitting on top of a rectangle. A(Triangle) = 1/2*3*12 + A(Rectangle) = 2*12 Total = 42. I don't know how to insert figures here so can't explain properly

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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10 Sep 2013, 11:25

Walkabout wrote:

Attachment:

Trapezoid.png

The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

(A) 39 (B) 40 (C) 42 (D) 45 (E) 46.5

If the trapezoid represents a cross section of the rudder of a ship, then the area of the cross section of the rudder in square feet should have been the area of both the triangles represented in the figure. I know I am obviously wrong here but the way I mentioned is stuck in my head.

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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11 Sep 2013, 02:54

Expert's post

aakrity wrote:

Walkabout wrote:

Attachment:

Trapezoid.png

The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

(A) 39 (B) 40 (C) 42 (D) 45 (E) 46.5

If the trapezoid represents a cross section of the rudder of a ship, then the area of the cross section of the rudder in square feet should have been the area of both the triangles represented in the figure. I know I am obviously wrong here but the way I mentioned is stuck in my head.

That's not wrong at all. But the area of a trapezoid can also be found with the direct formula as shown in posts above. If you expand that formula you'll see that you basically get the sum of the areas of the two triangles.

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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11 Sep 2013, 04:57

Bunuel wrote:

aakrity wrote:

Walkabout wrote:

Attachment:

Trapezoid.png

The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

(A) 39 (B) 40 (C) 42 (D) 45 (E) 46.5

If the trapezoid represents a cross section of the rudder of a ship, then the area of the cross section of the rudder in square feet should have been the area of both the triangles represented in the figure. I know I am obviously wrong here but the way I mentioned is stuck in my head.

That's not wrong at all. But the area of a trapezoid can also be found with the direct formulas as shown in posts above. If you expand that formula you'll see that you basically get the sum of the areas of the two triangles.

Does this make sense?

Oh right. Thank you. That is some relief definitely !

Re: The trapezoid shown in the figure above represents a cross [#permalink]

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