Question

Find the lateral area of a right triangular prism with an equilateralbase length of 5cm and height of 10cm.

Answer 1

Area = 3 equal rectangles + 2 equal equilateral triangles
the rectangels are easy, each is 5 by 10 or 50 cm^2

For the triangle, if you know two sides and the contained angle Ø between those sides, then the area
= (1/2)(side1)(side2)sinØ
we know it is equilateral so the angle is 60°
area of base triangle = (1/2)(5)(5)sin60°
= 25/2 (√3/2) = 25√3/4 cm^2

or

height of triangle:
h^2 + 25/4 = 25
h^2 = 75/4
h = √(75/4) = 5√3/2
area = (1/2)base x height = (1/2)(5)(5√3/2) = 25√3/4

add up the rectangles and triangles.