Question

What is the surface area of the right trapezoidal prism? To receive credit, you must show the work used to arrive at a final answer.

Answer 1

The total surface area of the right trapezoidal prism is 381
`cm^2`.

The total surface area of the right trapezoidal prism is the sum of the areas of the two bases and the four lateral faces.

Area of the bases:

The area of a trapezoid is calculated with the following formula:

Area of a trapezoid = 1/2 * (base 1 + base 2) * height

In this case, the bases of the trapezoid are 6 cm and 5 cm, and the height is 3 cm. Therefore, the area of each base is:

Area of each base = 1/2 * (6 cm + 5 cm) * 3 cm = 16.5
`cm^2`

As there are two bases, the total area of the bases is:

Total area of bases = 2 * 16.5
`cm^2` = 33
`cm^2`

Area of the lateral faces:

The lateral faces of a right trapezoidal prism are rectangles. The height of each rectangle is equal to the height of the prism (3 cm), and the width is equal to the perimeter of the trapezoid.

The perimeter of the trapezoid is the sum of the lengths of all its sides. In this case, the sides of the trapezoid are 6 cm, 5 cm, 11 cm, and 7 cm. Therefore, the perimeter of the trapezoid is:

Perimeter of the trapezoid = 6 cm + 5 cm + 11 cm + 7 cm = 29 cm

Therefore, the area of each lateral face is:

Area of each lateral face = height * perimeter = 3 cm * 29 cm = 87
`cm^2`

As there are four lateral faces, the total area of the lateral faces is:

Total area of lateral faces = 4 * 87
`cm^2` = 348
`cm^2`

Total surface area:

Finally, to find the total surface area of the right trapezoidal prism, we need to add the area of the bases and the area of the lateral faces:

Total surface area = total area of bases + total area of lateral faces

Total surface area = 33
`cm^2` + 348
`cm^2` = 381
`cm^2`

Therefore, the total surface area of the right trapezoidal prism is 381
`cm^2`.

Answer 2

210 cm²

Explanation:

The net of the right trapezoidal prism consists of 2 trapezoid base and four rectangles.

Surface area of the trapezoidal prism = 2(area of trapezoid base) + area of the 4 rectangles

✔️Area of the 2 trapezoid bases:

Area = 2(½(a + b)×h)

Where,

a = 7 cm

b = 11 cm

h = 3 cm

Plug in the values

Area = 2(½(7 + 11)×3)

= (18 × 3)

Area of the 2 trapezoid bases = 54 cm²

✔️Area of Rectangle 1:

Length = 6 cm

Width = 3 cm

Area = 6 × 3 = 18 cm²

✔️Area of Rectangle 2:

Length = 7 cm

Width = 6 cm

Area = 7 × 6 = 42 cm²

✔️Area of Rectangle 3:

Length = 6 cm

Width = 5 cm

Area = 6 × 5 = 30 cm²

✔️Area of Rectangle 4:

Length = 11 cm

Width = 6 cm

Area = 11 × 6 = 66 cm²

✅Surface area of the trapezoidal prism = 54 + 18 + 42 + 30 + 66 = 210 cm²