Answer
Total Surface Area of the prism = 240 cm²
Explanation
The total surface area is the sum of all the area of the faces of this prism.
The prism has two triangular faces and three rectangular faces.
Area of one triangle = ½bh
b = base of the triangle = 8 cm
h = perpendicular height of the triangle = 3 cm
Area of one triangle = ½bh
Area of one triangle = ½ (8) (3) = 12 cm²
Area of two triangles = 2 (12) = 24 cm²
Area of rectangle at the base = LW
L = length of the triangle = 12 cm
W = width of the triangle = 8 cm
Area of rectangle at the base = LW
Area of rectangle at the base = (12) (8) = 96 cm²
For the two triangles at the side of the prism, we need to find the width using pythagoras theorem
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For the triangles,
a = Half of 8 = 4 cm
b = 3
hyp = W = ?
a² + b² = (hyp)²
4² + 3² = W²
16 + 9 = W²
W² = 25
Take the square root of both sides
W = 5
Area of rectangle at the side = LW
L = length of the triangle = 12 cm
W = width of the triangle = 5 cm
Area of rectangle at the side = LW
Area of rectangle at the side = (12) (5) = 60 cm²
Area of two rectangles at the side = 2 (60) = 120 cm²
Total Surface Area of the prism = (Area of the two triangles) + (Area of the two rectangles on the side) + (Area of the rectangle at the bottom)
Area of the two triangles = 24 cm²
Area of the two rectangles on the side = 120 cm²
Area of the rectangle at the bottom = 96 cm²
Total Surface Area of the prism = (Area of the two triangles) + (Area of the two rectangles on the side) + (Area of the rectangle at the bottom)
Total Surface Area of the prism = 24 + 120 + 96 = 240 cm²
Hope this Helps!!!
