Given: The dimension as shown in the image
[tex]\begin{gathered} base(a)=20in \\ height(h)=10.5in \end{gathered}[/tex]
To determine: The name of the shape and the surface area
Solution
The name of the shape is a square-based pyramid
The area of a square-based pyramid can be calculated using the formula below
[tex]\begin{gathered} A=a^2+2a\sqrt{\frac{a^2}{4}+h^2} \\ A=Area \\ a=base-edge \\ h=height \end{gathered}[/tex]
Substitute the given dimension into the formula
[tex]\begin{gathered} A=20^2+2\times20\sqrt{\frac{20^2}{4}+10.5^2} \\ A=400+40\sqrt{\frac{400}{4}+110.25} \\ A=400+40\sqrt{210.25} \\ A=400+40(14.5) \\ A=400+580 \\ A=980in^2 \end{gathered}[/tex]
Hence, the name of the shape is a square-based pyramid and the surface area is 980in²
