SOLUTION: HI PLEASE HELP A right prism has a base in the shape of a right isosceles triangle with hypotenuse measuring 8.5 cm. The height of the prism is 12 cm. Round answers to the near

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Question 1154447: HI
PLEASE HELP
A right prism has a base in the shape of a right isosceles triangle with hypotenuse measuring 8.5 cm. The height of the prism is 12 cm. Round answers to the nearest ten.
(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%282%29 times the other side. Hence the two equal sides of the base triangle measure = 8.5+%2F+sqrt%282%29 = 6.01 cm.
Area of the base triangle = 0.5+%2A+6.01+%2A+6.01+=+18.06cm2
Volume of the prism = base area * height = 18.06+%2A+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
cm2 (rounded off to nearest 10th decimal)
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(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%282%29 times the other side. Hence the two equal sides of the base triangle measure = 8.5+%2F+sqrt%282%29 = 6.01 cm.
Area of the base triangle = 0.5+%2A+6.01+%2A+6.01+=+18.06cm2
Volume of the prism = base area * height = 18.06+%2A+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
cm2 (rounded off to nearest 10th decimal)