Question

Please help me with the question below (also please explain).

Answer 1

Given:

Shape is:

Find-:

The surface area of the shape

Explanation-:

The surafce area of a shape is:

$=AGED+CDEF+ABIG+ABCD+EGIF+CJHF+CJB+FHI+JHIB$

the surface area is:

$\begin{gathered} AGED=\text{ Length }\times\text{ Width} \\ \\ AGED\text{ }=12\times8 \\ \\ AGED=96 \end{gathered}$

The area of CDEF and ABIG is the same because of the same dimension.

$\begin{gathered} CDEF=ABIG \\ \\ CDEF=\text{ Length}\times\text{ Width} \\ \\ CDEF=12\times6 \\ \\ CDEF=72 \end{gathered}$

The area of ABCD and EFIG is the same because of the same dimension.

$\begin{gathered} ABCD=EFIG \\ \\ ABCD=\text{ Length }\times\text{ Width} \\ \\ ABCD=8\times6 \\ \\ ABCD=48 \end{gathered}$

The area of CJHF and JHIB is the same because of the same dimension.

$\begin{gathered} CJHF=JHIB \\ \\ CJHF=\text{ Length }\times\text{ Width} \\ \\ CJHF=12\times5 \\ \\ CJHF=60 \end{gathered}$

The area of CJB and FHI is the same because of the same dimension.

The area of a triangle is:

$\text{ Area }=\frac{1}{2}\times\text{ base}\times\text{ height}$

For triangle base and height is:

$\begin{gathered} \text{ Base }=8 \\ \\ \text{ Height }=3 \end{gathered}$

Area of CJB and FHI is:

$\begin{gathered} CJB=FHI \\ \\ CJB=\frac{1}{2}\times\text{ Base}\times\text{ Height} \\ \\ CJB=\frac{1}{2}\times8\times3 \\ \\ CJB=12 \end{gathered}$

So, the surface area is:

$\begin{gathered} =96+72+72+48+48+60+60+12+12 \\ \\ =480 \end{gathered}$

The surface area is 480 cm²