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an isosceles prism is a solid figure that has an isosceles triangle as its base.
the bases of the isosceles prism are connected by vertical lines emanating from each vertex of the corresponding angle of each base.
you are given that each base has sides of 15 cm, 15 cm, and 18 cm.
you are also given that the height of the prism is 25 cm.
apparently you are looking for the surface area of the prism.
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 formula for the area of a triangle is equal to 1/2 * the base of the triangle * the height of the triangle.
finding the surface area of each face of the prism is fairly easy.
the height is 25 cm .
2 of the faces will have a width of 15 cm.
1 of the faces will have a width of 18 cm.
the total surface area of the faces will be:
(25 * 15 * 2) + (25 * 18) = 750 + 450 = 1200 square cm.
the area of each of the bases requires a little more work.
the area of a triangle is equal to 1/2 * b * h.
this means 1/2 * the base times the height.
the base of the isosceles is 18 cm.
the height of the isosceles triangle needs to be determined.
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.
each side of that perpendicular will form a right triangle with a hypotenuse of 15 and a base of 9.
you can use the pythagorean formula to find the height of the perpendicular.
it turns out to be 12 because:
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.
the height of your isosceles triangle is equal to 12.
the area of each of your isosceles triangles is equal to 1/2 * 18 * 12 = 9 * 12 = 108 square cm.
you have 2 bases for a total surface area of 216 for the bases.
the total surface area of your triangular prism is therefore equal to 1200 + 216 = 1416 square cm.
the diagram shown below should help you to visualize what i just said above.
In the diagram below:
triangle ABC is the first base (b1)
triangle DEF is the second base (b2)
rectangle ABED is the first face (f1)
rectangle CBEF is the second face (f2)
rectangle ADFC is the third face (f3)
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.