![]() S 1 and S 2 are the three sides of the base triangleĪlso Read: Angle Sum Property of QuadrilateralĪ right triangular prism with equilateral bases and square sides is called a uniform triangular prism. Thus, adding all the areas, the total surface area of a right triangular prism is given by, Lateral surface area is the product of the length of the prism and the perimeter of the base triangle = (S 1 + S 2 + h) × l. Lateral Surface Area = (S 1 + S 2 + S 3 ) × LĪ right triangular prism has two parallel and congruent triangular faces and three rectangular faces that are perpendicular to the triangular faces.Īrea of the two base triangles = 2 × (1/2 × base of the triangle × height of the triangle) which simplifies to 'base × height' (bh). Thus, the lateral surface area of a triangular prism is: It is the sum of all the areas of the vertical faces. Lateral Surface area is the surface area of the prism without the triangular base areas. S 1, S 2, and S 3 are the three sides of the base triangle Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)ī is the resting side of the base triangle, Thus, the formula for the surface area of a triangular prism is: ![]() The area of the two triangular bases is equal to The sum of areas of the parallelograms joining the triangular base is equal to the product of the perimeter of the base and length of the prism. The surface area of a triangular prism is obtained by adding all the surface areas of faces that constitute the prism. Therefore, 84 square feet of cloth is required for a tent.Derivation of Surface Area of Triangular Prism 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. To calculate the surface area of triangular prisms, you need to calculate the area of each face and add them all together. ![]() 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. = 6 \(\times\) 4 + (5 + 6 + 5) \(\times\) 15 The surface area of a triangular prism is the sum of the areas of its 3 lateral faces and 2 bases and is given by the formula, where SA is surface area, a, b and c are the lengths of the sides of the bases, b is the bottom side of the base, and h is the height of the base. 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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