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Pyramid is a three-dimensional geometric shape with a convex polygonal base, triangular faces, and a common vertex. Pyramids come in various types, named according to their bases.
A triangular pyramid has a triangular base, and a quadrilateral pyramid has a quadrilateral base. In special cases like equilateral triangular or square bases, they're termed as regular pyramids. We'll now share how to calculate the surface area of a pyramid, corresponding to specific cases.
HOW TO CALCULATE THE SURFACE AREA OF A PYRAMID
The surface area of a pyramid includes the lateral surface area and the total surface area.
+ Surface area of a pyramid's lateral faces: Sxq = p.d (The surface area of a pyramid's lateral faces is half the product of its base perimeter and slant height).
Where: p is half the base perimeter, and d is the slant height of the pyramid. The slant height is the height drawn from the apex to the midpoint of an edge.
+ Total surface area of the pyramid: Stp = Sxq + Sbase
Therefore, to calculate the lateral and total surface areas of the pyramid, you need to calculate the length of the slant height and the base perimeter, and area. Here are specific exercises applying the formula above.
Exercise 1: Given a regular triangular pyramid with a base edge length of 6 cm and side lengths of 5 cm each. Calculate the lateral and total surface areas.
Solution:
Problem for a regular triangular pyramid, hence the pyramid base will be an equilateral triangle with side length 6 cm, and the side lengths are 5 cm.
To calculate the lateral and total surface areas of the pyramid, we need to find the length of the pyramid's slant height.
Draw a regular triangular pyramid SABC as shown in the image. From vertex S, draw a line to the midpoint of segment AC, denoted as point M. SM is the slant height of the pyramid.
Considering triangle SBM, since SBC is an isosceles triangle, SBM is a right triangle. Applying the Pythagorean theorem to this triangle, we find the length of SM. SM2 = SB2 - BM2 = 52 - 32 => SM = 4 cm.
The lateral surface area of the pyramid is: Sxq = p.d = 1⁄2 x 5 x 4 x 4 = 20 cm2
The total surface area of the pyramid is: Stp = Sxq + Sbase = 20 + 52 = 45cm2
Various exercises related to calculating the surface area of a pyramid exist. Mastering the calculation of triangle, quadrilateral, or rectangular areas will make calculating pyramid surface areas easier.
We hope this article, along with specific examples provided, helps you reinforce your knowledge of solid geometry. If you have any further questions, feel free to comment, and we'll be happy to assist you.
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A cone is also an interesting solid geometric shape. Refer to how to calculate the surface area of a cone here.
