![]() The formula to find the height of the altitude of the isosceles triangle is based on the pythagorean formula of hypotenuse squared is equal to the sum of each leg squared. The diagram shown below should help you to visualize what i just said above. The total surface area of your triangular prism is therefore equal to 1200 + 216 = 1416 square cm. You have 2 bases for a total surface area of 216 for the bases. ![]() The area of each of your isosceles triangles is equal to 1/2 * 18 * 12 = 9 * 12 = 108 square cm. The height of your isosceles triangle is equal to 12. H^2 + 9^2 = 15^2 which becomes h^2 + 81 = 225 which becomes h^2 = 225 - 81 which becomes h^2 = 144 which gets you h = 12 once you take the square root of both sides of that equation. You can use the pythagorean formula to find the height of the perpendicular. If you drop a perpendicular from the vertex opposite the base of the isosceles triangle, it will divide the base of the isosceles triangle into 2 equal parts.Įach side of that perpendicular will form a right triangle with a hypotenuse of 15 and a base of 9. The height of the isosceles triangle needs to be determined. This means 1/2 * the base times the height. ![]() The area of a triangle is equal to 1/2 * b * h. The area of each of the bases requires a little more work. The total surface area of the faces will be: The formula for the area of a triangle is equal to 1/2 * the base of the triangle * the height of the triangle.įinding the surface area of each face of the prism is fairly easy.Ģ of the faces will have a width of 15 cm.ġ of the faces will have a width of 18 cm. Isosceles Triangle Isosceles TriangleIsosceles triangles have at least 2. You need to find the area of each of the vertical faces of the prism plus the area of each of the bases of the prism. The base angles in an isosceles trapezoid are equal in measurement, also I know. You are also given that the height of the prism is 25 cm.Īpparently you are looking for the surface area of the prism. You are given that each base has sides of 15 cm, 15 cm, and 18 cm. The bases of the isosceles prism are connected by vertical lines emanating from each vertex of the corresponding angle of each base. This article has been viewed 680,987 times.You can put this solution on YOUR website!Īn isosceles prism is a solid figure that has an isosceles triangle as its base. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. There are 9 references cited in this article, which can be found at the bottom of the page. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. ![]() David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. Solve the area of a triangle formula, A ()bh for h. This article was co-authored by David Jia. As we know that the octagon consists of the 8 isosceles triangles so the area of one triangle will be.
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