- The lateral area is given by the formula:
[tex]A=Perimeter\times height[/tex]
Where:
Perimeter = 15 + 17 + side triangle
Height = 26 in26
First, we find the length of other side using the pythagoras theorem:
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2+15^2=17^2 \\ a^2+225=289 \\ a^2+225-225=289-225 \\ a^2=64 \\ a^=\sqrt{64} \\ a=8 \end{gathered}[/tex]
Therefore the perimeter is:
[tex]P=15+17+8=40\text{ in}[/tex]
And the lateral area is:
[tex]A=40\times26=1040\text{ in}^2[/tex]
- The surface area is given by
[tex]A=lateal\text{ area+2\lparen area triangle\rparen}[/tex]
Then, the area of the triangle is:
[tex]Atriangle=\frac{bh}{2}=\frac{8\times17}{2}=\frac{136}{2}=68\text{ in}^2[/tex]
So, the surface area is:
[tex]A=1040+2(68)=1040+136=1176\text{ in}^2[/tex]
Answer:
Lateral area = 1040 in^2
Surface area = 1176 in^2
