![]() Therefore, 84 square feet of cloth is required for a tent. Area Length (a + b + c) + (2 basearea) The a, b and c letters are the respective sides of the triangle. While the length is, you guessed it, the prism’s length. Since the kaleidoscope is in the shape of a triangular prism, we can use the formula for the surface area to find its height.ĥ76 = 9 \(\times\) 7.8 + (9 + 9 + 9)H ĥ76 – 70.2 = (27)H The most basic two equations are as followed: Volume 0.5 b h length b is the length of the triangle’s base. It is mentioned that the surface area of the kaleidoscope is 576 \(cm^2\) and the base height is 7.8 cm. Find the height of the kaleidoscope.Īs stated, the length of each side of the kaleidoscope is 7.8 cm. The surface area of the kaleidoscope is 576 \(cm^2\), and its base height is 7.8 cm. Hence, the surface area of a triangular prism is 264 square centimeters.Ĭathy recently purchased a new triangular kaleidoscope in which the sides are 9 cm long. Surface area of a triangular prism = bh + (a + b + c)H We can find the surface area of the triangular prism by applying the formula, ![]() The height of the triangular prism is H = 15 cm The base and height of the triangular faces are b = 6 cm and h = 4 cm. Where h is the height of a prism, A B is the base area, and P B is the perimeter of the prism base, the total surface area of a prism can be calculated using the following formula:īut we have to customize this formula to suit a rectangle since a rectangular prism has the base of a rectangle.Find the surface area of the triangular prism with the measurements seen in the image.įrom the image, we can observe that the side lengths of the triangle are a = 5 cm, b = 6 cm and c = 5 cm. Lateral surface area of the Rectangular Prism Ph 2h ( l + b) Total Surface area of Rectangular Prism 2B + Ph 2 ( lb + bh + hl) Volume of a rectangular prism Base area x height base width x base length x height. Then substitute into your formula and solve.Ī P t = ( 6 m × 4 m ) + 3 m ( 5 m + 6 m + 5 m ) A P t = ( 24 m 2 ) + 3 m ( 16 m ) A P t = 24 m 2 + 48 m 2 A P t = 72 m 2 What is the surface area of a rectangular prism?Ī rectangular prism is called a cuboid if it has a rectangular base or a cube if it has a square base with the height of the prism equal to the side of the square base. ![]() The total surface area of a triangular prism A Pt isĪnd c is also 5 m (Isosceles triangular base) This would even be more stressful as the number of sides increases.įind the total surface area of the figure below.Ĭalculating the surface area of a triangular prism, Vaia Originals This means we have to calculate the area of each rectangle. So, the area of the base and top is twice the base area. So, we can say that the total surface area of both the top and base of the prism isĪ B = b a s e a r e a A T = t o p a r e a A T B = A r e a o f b a s e a n d t o p A B = A T A T B = A B + A T A T B = A B + A B A T B = 2 A B The area of the top must surely be the same as the base area which depends on the shape of the base. We have 2 identical sides which take the shape of the prism, and n rectangular sides - where n is the number of sides of the base. Now that we know what the surfaces of a prism comprise, it is easier to calculate the total surface area of a prism. Likewise, a pentagonal base prism will have 5 other sides apart from its identical top and base, and this applies to all prisms.Īn illustration of the rectangular faces of a prism using a triangular prism, Vaia OriginalsĪlways remember that the sides which are different from the top and base are rectangular - this will help you in understanding the approach used in developing the formula. For instance, a triangular base prism will have 3 other sides aside from its identical top and base. It also comprises rectangular surfaces depending on the number of sides the prism base has. Triangular PrismĪ triangular prism has 5 faces including 2 triangular faces and 3 rectangular ones.Īn image of a triangular prism, Vaia Originals Rectangular PrismĪ rectangular prism has 6 faces, all of which are rectangular.Īn image of a rectangular prism, Vaia Originals Pentagonal PrismĪ pentagonal prism has 7 faces including 2 pentagonal faces and 5 rectangular faces.Īn image of a pentagonal prism, Vaia Originals Trapezoidal PrismĪ trapezoidal prism has 6 faces including 2 trapezoidal faces and 4 rectangular ones.Īn image of a trapezoidal prism, Vaia Originals Hexagonal PrismĪ hexagonal prism has 8 faces including 2 hexagonal faces and 6 rectangular faces.Īn image of a hexagonal prism, Vaia Originals In general, it can be said that all polygons can become prisms in 3D and hence their total surface areas can be calculated. There are many different types of prisms that obey the rules and formula mentioned above. The total surface area of a prism is the sum of twice its base area and the product of the perimeter of the base and the height of the prism.
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