In 7th grade, surface area is a brand new concept, so students will need time to understand what surface area is. If there are more quadrilaterals, then you have a triangular prism. To help students, ask, “Are there more triangles or quadrilaterals?” If there are more triangles, then you have a pyramid. Students sometimes struggled with differentiating between pyramids and triangular prisms. This will be an important distinction when they transition to calculating volume in later units. It is important to differentiate between the lateral height (which is the height of the triangular face) and the height of the pyramid. Pyramids have one base and the lateral faces all come to one point, the vertex. The pyramid is named by the shape of the base – so triangular prisms have a triangle base while rectangular pyramids have a square or rectangle as a base. Pyramids are included in 7th grade TEKS and 7th grade CCSS.Ī pyramid is composed of a base and triangular faces. This is a great time to rapidly cold call students to ask what each variable represents. Total Surface Area = Lateral Area + Area of Baseįor a cylinder, we can also develop formulas from the net.You will need to repeat the phrases, “perimeter of the base,” “area of the base” and “height of the prism” until you lose your voice. To find the total surface area, add the area of the base, B, to the lateral area. Lateral Area = 1 2 \frac × Perimeter of Base × Slant Height of Pyramid The area of the 4 lateral faces is found by adding the widths of all of the individual faces, the perimeter ( P) of the base of the pyramid, and then multiplying by the height of the triangle, which is the slant height, l, of the pyramid. Total Surface Area = Lateral Area + 2 × Area of Base To find the total surface area, add the area of the large rectangle plus two times the area of the base, B. Next, find the area of one of the two congruent bases, area B. Lateral Area = Perimeter of Base × Height of Prism The area of the big rectangle is found by adding the widths of all of the individual faces, the perimeter ( P) of the prism, and then multiplying by the height. The diagram shows the lateral faces of the prism forming one big rectangle. We know that the area of a rectangle is the product of the length and the width, so if we label the dimensions of each of the faces of the prism, we can calculate the surface area of the prism. The bases of the prism are highlighted in blue. Now that you have explored nets of 3-dimensional figures, let's use those nets to generate formulas for surface areas of prisms, pyramids, and cylinders.įirst, consider the net below for a rectangular prism. The barn is a prism with a seven-sided polygon as the base, so we can call the barn a heptagonal prism. ![]() The silo is in the shape of a cylinder with a half-dome roof. Since the surfaces of a cylinder are not polygons (they have round edges and are not always planar figures), we call them surfaces instead of faces.Ĭonsider the barn and silo shown. A cylinder has two circular bases and a curved lateral surface. A pyramid with a square base is called a square pyramid.Ī cylinder is like a prism, but the bases of a cylinder are circles instead of polygons. Like prisms, pyramids are named by the shape of their base. The lateral faces of a pyramid are triangles that meet at one point, which is called the vertex. Likewise, a prism with a hexagonal-shaped base is called a hexagonal prism.Ī pyramid is a 3-dimensional figure that has one base. So, a prism with a rectangular-shaped base is called a rectangular prism. ![]() ![]() A prism is named by the shape of its base. The lateral faces of a prism are always parallelograms and are usually rectangles. 3-dimensional figures occur everywhere in the world around us, especially in fields such as architecture.Ī prism is a 3-dimensional figure that has two parallel, congruent bases connected by lateral faces.
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