Use the image to answer the question.
An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as three vertical rectangles placed vertically. The length and width of the top rectangle are 6.5 feet and 5 feet respectively. The length and width of the middle rectangle are 5.5 feet and 5 feet respectively. The length of the bottom rectangle is 5 feet. Two identical triangles adjoin the middle rectangle on both sides with legs measuring 3.5 feet and 5.5 feet. The hypotenuse measures 6.5 feet.
Write an equation for the surface area of both triangular bases of the net.
A: SA=(12)(5)(6.5)
B: SA=2(12)(6.1)(3.5)
C: SA=12(3.5)(5)
D: SA=2(12)(3.5)(5.5)
D: SA=2(12)(3.5)(5.5)
The correct answer is:
D: SA=2(12)(3.5)(5.5)
The surface area of both triangular bases of the net can be calculated using the formula SA = 2*(base)*(height), where the base is the length of one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
In this case, the base of the triangle is 5.5 feet and the height can be calculated using the Pythagorean theorem as √(6.5^2 - 3.5^2) = √(42.25 - 12.25) = √30 = 5.5 feet.
Therefore, the equation for the surface area of both triangular bases of the net is SA = 2*(12)*(3.5)*(5.5).