Total Surface Area Lateral Area Area of Bases+2 11( )( ) ( )( ) + +72 34 34 22 7266++ 84 cm2 There is a bit of a shortcut for finding the lateral area of a prism. See examples, diagrams, and a lesson on the derivation of the formula. The total surface area of the triangular prism is the lateral area plus the area of the two bases. Therefore, 84 square feet of cloth is required for a tent. Learn how to calculate the surface area of a triangular prism using a formula that combines the areas of the base triangle and the three rectangular faces. 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 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. Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. = 6 \(\times\) 4 + (5 + 6 + 5) \(\times\) 15 Now, lets fill in the measurements for the sides of each face in order to calculate their area. 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. 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.
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