The formula for the volume of a rectangular prism with base $R$ is $ \times h$. Similarly, the process for deducing the volume of a cylinder mirrors very closely that for computing the area of circle by approximating with polygons, and then making an informal limit argument as the number of sides of the polygon goes to infinity (as presented for example in ). In part (b), students need to recognize that every polygon can be dissected into triangles, a fact students will find intuitively obvious after some experimentation, but which is not entirely trivial to carefully justify (although it is easy for convex polygons - you can explicitly construct the triangles by drawing lines from one given vertex to each non-adjacent vertex). For part (a), the argument relies on knowledge of 6.G.1 where the area of polygons is calculated by decomposing into triangles or composing to make rectangles. Students will likely need help understanding the level of rigor expected in these arguments. Depending on students' previous experience, some of these results could be taken for granted and then more time can be invested in part (b) of the task. J Need help with finding the volume of a triangular prism You're in the right placeWhethe. In the case of a triangular prism, the base area is the area of the triangular base, which can be calculated using Heron’s formula (if the lengths of the sides of the triangle are known) or by using the standard area of a. Welcome to How to Find the Volume of a Triangular Prism with Mr. In solution to part (a), substantial time is taken explaining how to find the area of a polygon (and hence the volume of a prism with polygon base) by triangulating the polygon: this fits well with the ''use dissection arguments'' part of the G-GMD.1 standard. The volume of any prism is equal to the product of its cross section (base) area and its height (length). When the side lengths are whole numbers (with a particular choice of units) the formula for prisms comes from the meaning of multiplication and more generally it can be deduced from the whole number case. Students encounter these formulas in eighth grade (8.G.9) but arguments based on dissections are introduced in high school. The goal of this task is to establish formulas for volumes of right prisms and cylinders.
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