Find The Surface Area Of A Right Triangular Prism Formula Geometry for Beginners – How To Find the Surface Area and Volume of Prisms

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Geometry for Beginners – How To Find the Surface Area and Volume of Prisms

Welcome to Geometry for Beginners. In this article, we’re starting to look at the 3-dimensional equivalents of the 2-dimensional relationships of perimeter and area. The perimeter of a polygon refers to the “distance around” while the area of ​​a polygon refers to the “space within”. For 3-dimensional figures, such as prisms, the “surrounding distance” is the surface area; And the “space inside” becomes the volume. We will present formulas for finding both the surface area and volume of a prism and discuss the use of these concepts.

Before we discuss formulas, we need to make sure that we are all painting the same type of figure. Let’s use a cereal box for our mental image. Our cereal box is an example Right rectangular prism. the right Because the sides (Lateral faces) is perpendicular to the top and bottom (The bases). rectangle Because that The bases (above and below) are rectangles. PRISM Because the figure has two equal polygonal bases that are parallel to each other and 4 lateral faces that are rectangles.

Note: If the sides were not perpendicular to the bases, the figure would be OBLIQUE–not right, and the lateral faces would be parallelograms instead of rectangles. If the sides of an oblique triangular prism are not perpendicular to the bases, the bases will be triangles, and the 3 lateral faces will be parallelograms.

Again, when painting our cereal box, the surface area will refer to the packaging or the box itself. For package manufacturers, the amount of material required for each box is extremely important. The grain inside the box represents the volume of the package, assuming the box is full. This is an equally important business concern.

The formulas for surface area and volume will look unusual because they use symbols we haven’t used before, but the symbols are just new. You already have the skills to use these formulas!

Formula for surface area of ​​a prism: SA = 2B + LAwhere SA is the surface area, B is area of baseand LA is the lateral area.

Therefore, to calculate the surface area of ​​a prism, we must calculate the area B of whatever polygon forms the base using the appropriate formula for shape. Then, this value must be multiplied by two because there are 2 bases.

Next, we must calculate the lateral area which is the sum of the areas of the sides. Since the sides are either a rectangle or a parallelogram, we will use the formula A = bh. Then join the sides together for the lateral area. Be careful! Be sure you are using actual height and if the sides are parallelograms.

The last step is to add your values ​​of 2B and LA.

SA = 2B + LA is the best way to memorize and read the formula “The surface area of ​​a prism is equal to twice the sum of the area of ​​the base and the area of ​​all lateral sides.” Note that area is always labeled as a square unit.

Formula for volume of prism: V = Bhwhere, again, B is area of base and h is the height of the prism.

Be careful! Remember that the edge of a prism is the height Only if The figure is a right prism. If the prism is oblique, the height must be calculated as required in non-right triangles.

The formula should be read as V = Bh “The volume of a prism is equal to the area of ​​the base times the height of the prism.” Remember that volume is labeled as cubic units.

I guess you could say that these formulas are actually simple to calculate IF You have mastered the vocabulary and area formulas for 2-dimensional polygons. Secrets of Success in Geometry: Remember! Remember! Remember!

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