![]() ![]() From the formula in the above section, we find that: ![]() ![]() Using the notation in the calculator and on the picture, we have a = 6 in and b = 8 in. We'll try to follow the way the calculator thinks, and see how it arrives at the answer. Say that its base is 6 by 8 inches, and its height is 12 inches. Suppose we know how to find the volume of a rectangular pyramid. Okay, let's now get down to details and see our calculator in action. A scrupulous eye will notice that, in fact, among the four, we have two pairs of equal areas, and if the base is a square, all four of them are equal. Where the indexed A-s denotes the surface area of consecutive lateral faces. This way, we arrive at the not-so-scary-anymore formula: But worry not, my friend! As long as we know a and the pyramid height, we can calculate h using the Pythagorean theorem. We usually know a well enough, but h can get a little tricky. Let us now take care of the other faces of the pyramid and find the lateral area, A_l.Īt first glance, you might think that we might have a problem here since the lateral edges are triangles, whose surface area formula is area = (a × h) / 2, where a is the base length and h is the height projected onto that a, also called the slant of the pyramid. Observe that when we asked ourselves how to find the volume of a rectangular pyramid above, we had to know the base area of the pyramid, i.e., the value A_b. It seems that we weren't so far from the actual answer with our initial " probably a lot." ![]() Or roughly 3,390,339 cubic yards if you prefer imperial. Using the above square pyramid volume formula, we find that: Now we're left with the most fun part, counting! Yay, right? Right.? Moreover, we will need the height of the pyramid, so once again, we use our favorite search engine and find that it is 147 meters (or 280 Egyptian Royal cubits). (Also, in this case, please let us know how you do that pose that is on all your hieroglyphs because some of us have been trying to bend our hands that way since primary school, and we just can't get it right.) Otherwise, let's use the good old metric system – 230 meters. If you happen to be an ancient Egyptian, this is equal to 440 Egyptian Royal cubits. As you may know, the Great Pyramid of Giza's base is a square, so we will use the well-known formula of area = a × a, where a is the base side length. Note that we will need to know the base area. Volume = (base_area × pyramid_height) / 3. All the other cases can be calculated with our triangular prism calculator.Let's begin with a question that may have bugged you for years: what is the volume of the Great Pyramid of Giza? Unfortunately, " probably a lot" is often not a sufficient answer, so let's take a look at the square pyramid volume formula to see what we're dealing with: The only case when we can't calculate triangular prism area is when the area of the triangular base and the length of the prism are given (do you know why? Think about it for a moment). Using law of sines, we can find the two sides of the triangular base:Īrea = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2) Triangular base: given two angles and a side between them (ASA) Using law of cosines, we can find the third triangle side:Īrea = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle) Triangular base: given two sides and the angle between them (SAS) However, we don't always have the three sides given. area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area).If you want to calculate the surface area of the solid, the most well-known formula is the one given three sides of the triangular base : You can calculate that using trigonometry: Length * Triangular base area given two angles and a side between them (ASA) You can calculate the area of a triangle easily from trigonometry: Length * Triangular base area given two sides and the angle between them (SAS) If you know the lengths of all sides, use the Heron's formula to find the area of the triangular base: Length * Triangular base area given three sides (SSS) It's this well-known formula mentioned before: Length * Triangular base area given the altitude of the triangle and the side upon which it is dropped Our triangular prism calculator has all of them implemented. A general formula is volume = length * base_area the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. In the triangular prism calculator, you can easily find out the volume of that solid. ![]()
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