To write expressions for the surface area of a trapezoidal prism, you need to know the following:
The length of the prism (l)
The height of the prism (h)
The length of the bases of the trapezoid (a and b)
The length of the other two sides of the trapezoid (c and d)
The surface area of a trapezoidal prism is the sum of the areas of all of its faces. This includes the two trapezoidal faces and the four rectangular faces.
To write an expression for the surface area of a trapezoidal prism:
Find the area of each trapezoidal face. The area of a trapezoid is given by the following formula:
A = 1/2(b1 + b2)h
where b1 and b2 are the lengths of the bases of the trapezoid and h is the height of the trapezoid.
Find the area of each rectangular face. The area of a rectangle is given by the following formula:
A = lw
where l and w are the length and width of the rectangle.
Add the areas of all of the faces to find the total surface area of the trapezoidal prism.
Expression for the surface area of a trapezoidal prism:
Surface area = 2 * 1/2(b1 + b2)h + 4lw
Example:
Consider a trapezoidal prism with the following dimensions:
Length: l=10 units
Height: h=7 units
Base lengths: b1=4 units and b2=7 units
Other side lengths: c=4 units and d=3 units
The surface area of this trapezoidal prism can be calculated using the following expression:
Surface area = 2 * 1/2(4 + 7) * 7 + 4 * 10 * (4 + 7 + 4 + 3)
Surface area = 76.5 square units
You can also use the following formula to calculate the surface area of a trapezoidal prism:
Surface area = h(b1 + b2) + l(a + b1 + b2 + c)
where h is the height of the prism, b1 and b2 are the lengths of the bases of the trapezoid, l is the length of the prism, and a and c are the lengths of the other two sides of the trapezoid.
The two formulas are equivalent, so you can use whichever one you prefer.
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