Triangular prism

The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.

Result

S =  113.5 cm2

Solution:

b=5222=4.583 cm h=7/9(2+4.583+5)=9.009 cm S=2S1+S2+S3+S4 S=2ab2+ah+bh+ch S=ab+h(a+b+c) S=24.583+9.009(2+4.583+5) S=113.5 cm2b = \sqrt{ 5 ^2 - 2^2 } = 4.583 \ cm \ \\ h = 7/9\cdot ( 2+ 4.583 + 5 ) = 9.009 \ cm \ \\ S = 2S_1 + S_2 + S_3 + S_4 \ \\ S = 2 \cdot \dfrac{ab}{2} + ah + bh+ ch \ \\ S = ab + h(a + b+ c) \ \\ S = 2 \cdot 4.583 + 9.009( 2 + 4.583 + 5) \ \\ S = 113.5 \ \text{cm}^2



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