Question

Find the surface area of the polyhedron below. The area of each base is 65 cm2O A. 400 cm2O B. 130 cm?O c. 200 cm2O D. 330 cm2

Answer 1

Given: A polyhedron shown in the image

To Determine: The surface area of the polyhedron

Solution

It can be observed that the polyhedron has 6 faces and two base faces

Each of the sides are rectangle. The area of a rectangle can be calculated as

`Area(rectangle)=length* width`

So, for each of the 6 rectangular faces, the area is as calculated below

`\begin{gathered} Area(Rectangle1)=4cm*10cm=40cm^2 \\ Area(Rectangle2)=3cm*10cm=30cm^2 \\ Area(Rectangle3)=2cm*10cm=20cm^2 \end{gathered}`
`\begin{gathered} Area(Rectangle4)=2cm*10cm=20cm^2 \\ Area(Rectangle5)=2cm*10cm=20cm^2 \\ Area(Rectangle6)=7cm*10cm=70cm^2 \end{gathered}`

The area of the polyhedron is addition of all the areas of the rectangle and the two base area

`\begin{gathered} Area(Polyhedron)=65cm^2+65cm^2+40cm^2+30cm^2+20cm^2+20cm^2+20cm^2+70cm^2 \\ =330cm^2 \end{gathered}`

Hence, the area of the polyhedron is 330cm²