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The lateral surface area, L.A., of a regular pyramid is given by the formula,

L.A. = (1/2)nsl, where

n = number of the sides of the base

s = length of the each side of the base

l = slant height.

The surface area S.A. is given by the following formula.

S.A. = L.A. + B, where B is the area of the base.

In our problem,

n = 4

s = ?

l = 9 cm

L.A. = 270 cm2

So we have:

L.A. = (1/2)nsl

270 cm2 = (1/2)(4)(s)(9 cm)

270 cm = 18s

s = 270/18 cm

s = 15 cm

S.A. = L.A. + B

S.A. = = 270 cm2 + (15 cm)2

S.A. = 270 cm2 + 225 cm2

S.A. = 495 cm2

In the same way you will work to find the pentagonal base length side and the total area of a regular pyramid.

Q: A square based pyramid has a lateral area of 270cm and a slant height of 9cm. How do you find the length of a side of the pentagonal base and the total area?

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v= 1/2 * length * height * width Pyramid SolidSolving for volume:

429 m

If you make a line from the top of the pyramid to the center of the base, you have the height of the pyramid. This meets at the midsegment of a line going across the base. Since the height of a pyramid is perpendicular with the base, get this: the height, a line of 1/2 the length of the base, and the slant height form a right triangle. So, you can use the Pythagorean Theorem! For example, if the base length is 6 and the height of the pyramid is 4, then you can plug them into the Pythagorean Theorem (a squared + b squared = c squared, a and b being the legs of a right triangle and c being the hypotenuse). 1/2 the length of the base would be 6 divided by 2=3. 3 squared + 4 squared = slant height squared. 9+16=slant height squared. 25= slant height squared. Slant height=5 units. You're welcome!

Area of pentagon * length of prism.

35.2

Related questions

210 in 2

You need some information about the height of the pyramid and the formula will depend on whether you have the vertical height or the slant height or the length of a lateral edge.

It is 448 square cm.

72 cm square.

yes

LENGTH

The formula for the volume of a pyramid such as you described would be: V = 1/3Ah where A is the area of the base (a square in this case) and h is the height of the pyramid. You know the volume and the height, so you can plug them into that formula to solve for A, the area of the square base: 63690 = 1/3A(30). A = 6369 square meters. Knowing the area of the square, and the fact that the formula for the area of a square is A = s2 where s is the length of a side, you can find the length of s by taking the square root of 6369. s = about 79.8 meters. The next steps will require some thinking about what that pyramid looks like and what the length of a lateral height segment would represent. Drawing a diagram often helps. If I understand correctly what you mean by "lateral height segment" of the pyramid, meaning the length of the segment from the center of a side at the bottom to the vertex at the top, that length would represent the hypotenuse of a right triangle whose legs are 30 meters (the inside height of the pyramid) and about 39.9 meters (half the length of a side, in other words the distance from the point at the center of the base to the center of the side). You can use the Pythagorean theorem to find that length: c2 = a2 + b2 c2 = 302 + 39.92 c2 = 900 + 1592 c2 = 2492 c = 49.9 meters (approximately)

If it is a regular pyramid you need to find out the base perimeter, multiply it by the height of the sides (when considered as triangles) and divide by two. The height of the side can be found using Pythagoras's formula if you know the height of the pyramid and the length of a side. The side height of a pyramid is also known as the slanted height or L in a formula. Formula:permiter of base x L(side height) ( P of B)(L) p x L(slant) ----------------------------------------- = --------------------- 2 2 Good luck!

V = (1/3) (area of the base) (height) Area of a pentagon = 1/2 x apothem length x 5 x length of a side of the pentagonthe apothem is the perpendicular distance from the center of the pentagon to the side of the pentagon

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Its vertical height is that of the perpendicular from the centre of the base to the apex; the slant height is the length of the sloping "corner" between two faces. The height of a regular pyramid is the vertical distance from the center of base to the top and is usually shown with a line perpendicular to the base, denoted with a right angle to the base. The slant height it the height of the lateral face (the triangles) from the edge of the base to the top of the pyramid. It is the height of the triangle, not the pyramid itself. The slant height will also be the hypotenuse of a right angle formed from the altitude of the pyramid and the distance from the center of the base to the edge.

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