#Volume of a trapezoidal prism online how to

The perimeter of the base is the sum of the lengths of the sides. Solution: Using the Pythagoras theorem, the slant height or the non-parallel side = √(16+1) = √17 = 4.123 ft Step 5: Put the values in the formula, 2B + Lateral Surface Area(PH), to get the total surface area of the hexagonal prism.Įxample: Determine the total surface area of the trapezoidal prism.

Find the base area B by putting the above values in the formula, (b1+b2)h/2

Step 4: Identify b1 and b2 (lengths of the bases) of the trapezoid and h (height) of the trapezoid.

Step 3: Put the values in the formula, (a+b+c+d) × H or PH, to find the lateral surface area of the hexagonal prism.

Step 2: Identify the length H of the prism.

Add these 4 values in order to find the perimeter P.

Step 1: Identify the four sides of the trapezium - a, b, c, and d, representing the widths of the four rectangles.

Note that all measurements are of the same units. Here are the steps to calculate the surface area of a trapezoidal prism.

#Volume of a trapezoidal prism online how to

How to Calculate the Surface Area of a Trapezoidal Prism?

Thus, the total surface area of a trapezoidal prism is h(b+d)+l(a+b+c+d) square units. TSA of the trapezoidal prism = h (b + d) + l (a + b + c + d). Therefore, the total surface area of the trapezoidal prism (TSA) = 2 × h (b + d)/2 + (a × l)+(b × l) + (c × l) + (d × l) = h (b + d) + Substituting the values from equation (2) and equation (3) in the TSA formula, which is represented by equation (1): The lateral surface area of the trapezoidal prism (LSA) is the sum of the areas of each rectangular surface around the base that means, LSA = (a × l) + (b × l) + (c × l) + (d × l) - (3) Thus, the area of trapezoidal base = h (b + d)/2 - (2) We already know that the total surface area of the trapezoidal prism (TSA) = 2 × area of base + lateral surface area - (1)Īlso, the area of a trapezoid = height(base1 × base 2)/2.

l is the length of the trapezoidal prism.

h is the distance between the parallel sides.

We know that the base of a prism is in the shape of a trapezoid. #GK#, in the middle, is equal to #DC# because #DE# and #CF# are drawn perpendicular to #GK# and #AB# which makes #CDGK # a rectangle.Derivation of Surface Area of Trapezoidal Prism The large base is #HJ# which consists of three segments: Since we have to find an expression for #V#, the volume of the water in the trough, that would be valid for any depth of water #d#, first we need to find an expression for the large base of trapezoid #CDHJ# in terms of #d# and use it to calculate the area of the trapezoid. The volume of water is calculated by multiplying the area of trapezoid #CDHJ# by the length of the trough. This change affects the length of the large base of the trapezoids at both ends. The water in the trough forms a smaller trapezoidal prism whose length is the same as the length of the trough.īut the trapezoids in the front and the back of the water prism are smaller than those of the trough itself because the depth of the water #d# is smaller than the depth of the trough.Īs the water level varies in the trough, #d# changes. The water level in the trough is shown by blue lines. The volume of prism is calculated by multiplying the area of the trapezoid #ABCD# by the length of the trough.īut we are asked to figure out the volume of the water in the trough, and the trough is not full. The trough itself is a trapezoidal prism. The front and back of the trough are isosceles trapezoids. The figure above shows the trough described in the problem.