Surface Area of a Pyramid Lateral Area Geometry

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Surface Area of a Pyramid Lateral Area Geometry

The Organic Chemistry Tutor · ⏱ 3:28 · 272.1K مشاهدة · 8 years ago

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in this lesson we're going to talk about how to calculate the surface area of square based pyramid so how can we calculate the surface area of this pyramid we're going to say this is 10 that's 10 and the height of the pyramid that's going to be 12 units long so with this information calculate the total surface area of the pyramid so we need to calculate the area of the base and then add up the area of the four triangles so since we have square the area of the base is just squared or 10 squared which is 100. now the total surface area is the area of the base plus the lateral area so we have the area of the base that's 100. now we need to calculate the lateral area so notice that this forms right triangle and this represents the slant height now if this is 10 that means this section here has to be 5 and so if we focus on that right triangle if this side is 5 and this is 12 we have the 5 12 13 right triangle and you can use the pythagorean theorem to get that answer so squared is equal to squared plus squared is 5 is 12. 5 squared is 25 12 squared is 144 and so squared is equal to 169. if you take the square root of 169 that will give you 13 which is the slant height so this triangle here is basically this triangle that you see right here it's one of the four triangles so we have the slant height which is that's the height of this triangle that's 13 and the base of this triangle is 10. so now we can calculate the area of that triangle so the area is going to be one half base times height so the base is 10 the height is 13. half of 10 is 5 and 5 times 13 is 65 so that's the area for one triangle the lateral area is going to be the total area for all four triangles so it's going to be four times 65 which is 260. so that's the lateral area so to calculate the total area it's going to be the area of the base which is 100 plus the lateral area which is 260. so that's going to be 360 square units so that's how you can calculate the total surface area of pyramid you