Answer:
<h2><u><em>
504 sq.in.</em></u></h2>
Step-by-step explanation:
<u><em>Given,</em></u>
Edges of a box = 12 in. , 15 in. , 6 in.
<u><em>So,</em></u>
Lateral Surface Area (LSA) of the box
= 2 (l + b) h
- <em>[On substituting their values]</em>
= [2 (12 + 15) × 6 ] ![in^{2}](https://tex.z-dn.net/?f=in%5E%7B2%7D)
- <em>[On simplifying]</em>
= [2 × 27 × 6] ![in^{2}](https://tex.z-dn.net/?f=in%5E%7B2%7D)
= 324![in^{2}](https://tex.z-dn.net/?f=in%5E%7B2%7D)
<u><em>And,</em></u>
Base area of the box
= l × b
- <em>[On substituting the values]</em>
= (12 × 15) ![in^{2}](https://tex.z-dn.net/?f=in%5E%7B2%7D)
- <em>[On multiplying]</em>
= 180 ![in^{2}](https://tex.z-dn.net/?f=in%5E%7B2%7D)
<u><em>Therefore,</em></u>
Total area painted by Agnes leaving the top of the box
= LSA of the box + Base area of the box
- <em>[On putting their values]</em>
= 324
+ 180 ![in^{2}](https://tex.z-dn.net/?f=in%5E%7B2%7D)
= 504
<u><em>Hence,</em></u>
<u><em>The total area painted is 504</em></u>
<u><em> (Ans)</em></u>