Chapter 11.2, Problem 19E

To determine

To calculate: the surface area of prism

  

Answer to Problem 19E

The surface area of prism is $90$ square centimetre

Explanation of Solution

Given information: Consider, the values provided in the question

Height $=9$

Base $=4$

Formula used: Area of pyramid $=b^2$

Area of triangular $=\left(\frac{1}{2}\times base\times slantheight\right)$

Calculation: To evaluate

The area of four slant sides of pyramid

Area₁$=4\times \left(\frac{1}{2}\times 4\times \sqrt{85}\right)$

Area₁$=8\sqrt{85}$

The area of the base of pyramid

Area₂$=4\times 4$

Area₂$=4\times 4$

Total surface area of pyramid= Area₁₊ Area₂ Total surface area of pyramid $=16+8\sqrt{85}$

Total surface area of pyramid $=90$

The surface area of prism is $90$ square centimetre