To calculate we have to break down the shape into the respective surfaces
The area of a triangle is
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times base\times height \\ \text{where,} \\ \text{base}=28\operatorname{cm} \\ \text{height}=15\operatorname{cm} \end{gathered}[/tex]
Substituting the values, we will have
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times28\operatorname{cm}\times15\operatorname{cm} \\ \text{Area}=14\times15 \\ \text{Area}=210\operatorname{cm}^2 \end{gathered}[/tex]
Secondly, we will bring out the base
The area of a rectangle is
[tex]\begin{gathered} \text{Area}=\text{Length}\times breadth \\ \text{where,} \\ \text{length}=30\operatorname{cm} \\ \text{breadth}=28\operatorname{cm} \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=\text{Length}\times breadth \\ \text{Area}=30\operatorname{cm}\times28\operatorname{cm} \\ \text{Area}=840\operatorname{cm}^2 \end{gathered}[/tex]
Thirdly,
We will bring the out slant rectangular faces
The area of a rectangle is
[tex]\begin{gathered} \text{Area}=\text{Length}\times breadth \\ \text{where,} \\ \text{length}=30\operatorname{cm} \\ \text{breadth}=25\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} \text{Area}=30\operatorname{cm}\times25\operatorname{cm} \\ \text{Area}=750\operatorname{cm}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the second slant rectangular face=Length}\times breadth \\ \text{Area of the second slant rectangular face}=17\operatorname{cm}\times30\operatorname{cm}= \\ \text{Area of the second slant rectangular face}=510\operatorname{cm}^2 \end{gathered}[/tex]
Hence,
The total surface area of the solid prism will be
[tex]\begin{gathered} \text{Total}=\text{ (area of two triagular faces) + (area of the base) + (area of the rectangular slant faces)} \\ \text{Total surface area = }(2\times210cm^2)+(840\operatorname{cm})+(750\operatorname{cm})+(510\operatorname{cm}) \\ \text{Total surface area}=420\operatorname{cm}+840\operatorname{cm}+750\operatorname{cm}+510\operatorname{cm} \\ \text{Total surface area}=2,520\operatorname{cm}^2 \end{gathered}[/tex]
Hence,
The final answer is = 2,520cm²
