![]() If you're searching for a calculator for other 3D shapes – like e.g. Solve it manually, or find it using our calculator. That's again the problem solved by the volume of a rectangular prism formula. Your good old large suitcase, 30 × 19 × 11 inches or You have to pack your stuff for the three weeks, and you're wondering which suitcase □ will fit more in: You are going on the vacation of your dreams □. ![]() But how much dirt should you buy? Well, that's the same question as how to find the volume of a rectangular prism: measure your raised bed, use the formula, and run to the gardening center. For that, you need to construct a raised bed and fill it with potting soil. The time has come – you've decided that this year you'd like to grow your own carrots □ and salad □. It is a similar story for other pets kept in tanks and cages, like turtles or rats – if you want a happy pet, then you should guarantee them enough living space. If you're wondering how much water you need to fill it, simply use the volume of a rectangular prism formula. It's in a regular box shape, nothing fancy, like a corner bow-front aquarium. You bought a fish tank for your golden fish □. The surface area of the prism is 2 0 4 u n i t .Where can you use this formula in real life? Let's imagine three possible scenarios: Where □ and □ are its two parallel sides and ℎ its height. Let us work out the area of the base of the prism. We can of course work out the area of each rectangular face individually and sum up all together we find the same result. Its area is given by multiplying its length by its width. We clearly see on the net that they form a large rectangle of length the perimeter of the base and width the height of the prism, The lateral surface area of the prism is the area of all its rectangular faces that join the two bases. ![]() Rectangle whose dimensions are the height of the prism and the perimeter of the prism’s base. The surface area of a prism: on the net of a prism, all its lateral faces form a large In the previous example, we have found an important result that can be used when we work out The surface area of the prism is 7 6 u n i t . t o t a l b a s e l a t e r a l u n i t To find the total surface area of the prism, we simply need to add two times the area of theīase (because there are two bases) to the lateral area. We do find the same area however we compose rectangles to make the base. We can of course check that we find the same area with adding the area of two rectangles Or as the rectangle of length 5 and width 4 from which the rectangle of length The base can be seen as made of two rectangles, ![]() We need to find the area of the two bases. Prism, which is given by multiplying its length by its width: Now, we can work out the area of the large rectangle formed by all the lateral faces of the The missing lengths can be easily found given that all angles in the bases are right angles. The width of the rectangle formed by all lateral faces is actually the perimeter of the base. Where □ and □ are the two missing sides of the base of the prism. They form a large rectangle of length 3 and width We see that all the rectangles have the same length: it is the height of the prism, On the net, the rectangular faces between the two bases are clearly to be seen.
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