Question

I need help on question 4 which is the first one

Answer 1

Given: The dimension as shown in the image

`\begin{gathered} base(a)=20in \\ height(h)=10.5in \end{gathered}`

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

`\begin{gathered} A=a^2+2a\sqrt{(a^2)/(4)+h^2} \\ A=Area \\ a=base-edge \\ h=height \end{gathered}`

Substitute the given dimension into the formula

`\begin{gathered} A=20^2+2*20\sqrt{(20^2)/(4)+10.5^2} \\ A=400+40\sqrt{(400)/(4)+110.25} \\ A=400+40√(210.25) \\ A=400+40(14.5) \\ A=400+580 \\ A=980in^2 \end{gathered}`

Hence, the name of the shape is a square-based pyramid and the surface area is 980in²