Below is an example of how to use the space diagonal of a rectangular prism formula.Example 3: Comparing the Capacities of BoxesĪ man needs to store 16 170 cm 3 of rice in a container. Refer to the figure in the volume section above. Where l is length, w is width, and h is height. The rectangular prism space diagonal formula is Surface area is measured in squared units, so given that each edge is measured in feet, the rectangular prism has a total surface area of 276 ft 2. The total surface area is the sum of the areas of all the pairs of faces: Each base has an area of 6 × 4 = 24, so the two have an area of 48. To find the total surface area, we add the area of the two congruent bases. Since these areas only represent half of the area, we multiply by 2 to take into account their congruent counterparts and find that the lateral surface area of the rectangular prism is: The area of the right face is found by multiplying width and height to get 4 × 9 = 36. The area of the front face is found by multiplying the length and the height to get 6 × 9 = 54. In the figure, one of each pair of congruent faces is shaded (the front face and the right face). Recall that opposing faces of a rectangular prism are congruent. The length of the rectangular prism is 6, its width is 4, and its height is 9. For an oblique rectangular prism, the height is the perpendicular distance from any point on one base to the other base.īelow is a rectangular prism volume example.įind the surface area of the rectangular prism shown in the figure below. For a right rectangular prism, the height is its vertical edge. Where l is the length of the base, w is the width of the base, and h is the height of the prism. The figure below shows a cuboid example:Ī cube is a special case of a cuboid that shares all of the properties of a cuboid while also having edges that are all congruent.īelow are formulas for the volume, surface area, and space diagonals of a rectangular prism. In other words, all cuboids are rectangular prisms, but not all rectangular prisms are cuboids. In a rectangular prism, the lateral faces may be parallelograms which means that some of the faces do not meet at 90° angles. This is the key difference between a cuboid and a rectangular prism. All the faces of a cuboid meet at 90° angles. The figure below shows an oblique rectangular prism example:Ī cuboid is a 3D figure made up of 6 rectangular faces. This results in the lateral faces being parallelograms rather than rectangles, while the bases are still both rectangles. The figure below shows a right rectangular prism example:Īn oblique rectangular prism is a rectangular prism in which the bases and lateral faces are not perpendicular. As a result, all of the faces of a right rectangular prism are rectangles (this includes square bases or faces). In other words, all the faces meet at right angles (90°). Right rectangular prismĪ right rectangular prism is a rectangular prism in which the bases are perpendicular to its lateral faces. There are two rectangular prism types: right rectangular prisms and oblique rectangular prisms. The figure below shows two cross sections, shaded in purple, that are parallel and congruent to the bases of the rectangular prism.
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