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secondary 4 | E Maths
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A pyramid with a rectangular base 30cm × 18cm
Slant height of VAB is 15cm
i) prove that height is 12cm
ii) calculate the minimum area of decorative paper required to cover the entire solid.
Please help me
Date Posted: 3 years ago
Views: 199
See the previous question posted by user Daequan. It is the same question. I have posted the solution to ii) there.
As for part i),
let C be the centre of the rectangular base and Y be the midpoint of one of its lengths.
Triangle VCY is right angled so we can use Pythagoras' Theorem.
VY is just the slant height of the triangle ABV (and also the hypotenuse of △VCY)
VC is the height of the pyramid.
CY is parallel to the rectangle breadths but has only half their lengths.
So CY = ½(18cm) = 9cm
Now, using Pythagoras' Theorem,
VC² + CY² = VY²
VC² + 9² = 15²
VC² = 15² - 9² = 225 - 81 = 144
VC = √144 = 12
∴ Height of pyramid = 12cm
(Shown)
let C be the centre of the rectangular base and Y be the midpoint of one of its lengths.
Triangle VCY is right angled so we can use Pythagoras' Theorem.
VY is just the slant height of the triangle ABV (and also the hypotenuse of △VCY)
VC is the height of the pyramid.
CY is parallel to the rectangle breadths but has only half their lengths.
So CY = ½(18cm) = 9cm
Now, using Pythagoras' Theorem,
VC² + CY² = VY²
VC² + 9² = 15²
VC² = 15² - 9² = 225 - 81 = 144
VC = √144 = 12
∴ Height of pyramid = 12cm
(Shown)
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Understand pythagoras theorem and formula for area of pyramid to answer this type of question.
Date Posted:
3 years ago
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