Question 1154447

(a) What is the volume?
Base is in the form of a right isosceles triangle with hypotenuse = 8.5. Through Pythagoras theorem, we know that in a right isosceles triangle, the hypotenuse is {{{sqrt(2)}}} times the other side. Hence the two equal sides of the base triangle measure = {{{8.5 / sqrt(2)}}} = 6.01 cm.
Area of the base triangle = {{{0.5 * 6.01 * 6.01 = 18.06}}}cm2
Volume of the prism = base area * height = {{{18.06 * 12 = 216.75 = 216.8}}} cm3 - rounded to nearest 10th decimal place

(b) What is the total surface area?
Total surface area = 2 * area of base triangle + area of the 3 rectangles that form the vertical faces.
Area of base triangle = 18.06 cm2 as calculated earlier
Of the 3 vertical rectangles, all of them have the longer side as 12 cm (height of the prism). 2 of them have the shorter side as 6.01 cm and one has the shorter side as 8.5 cm. So the sum of the 3 areas is
{{{12 * 6.01 + 12 * 6.01 + 12 * 8.5 = 246.25 cm2
So the total surface area = {{{18.06 * 2 + 246.25 = 282.4}}} cm2 (rounded off to nearest 10th decimal)