Given:
In a given figure,
The length of the sides of the triangle is 4, 13, and 15.
The dimensions of one rectangle are 4 by 6.
The dimensions of one rectangle are 13 by 6.
The dimensions of one rectangle are 15 by 6.
To find:
The total surface area and volume.
Explanation:
The total surface area of the figure is,
[tex]A=2\times Area\text{ of the triangle+Area of the rectangle 1 + Area of the rectangle 2 +Area of the rectangle 3.}[/tex]
Using the heron's formula,
[tex]\begin{gathered} S=\frac{a+b+c}{2} \\ =\frac{4+13+15}{2} \\ =\frac{32}{2} \\ s=16 \end{gathered}[/tex]
The area of the triangle will be,
[tex]\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ A=\sqrt{16(16-4)(16-13)(16-15)} \\ A=24unit^2 \end{gathered}[/tex]
Therefore, the total surface area of the figure becomes,
[tex]\begin{gathered} TSA=2\times24+4\times6+13\times6+15\times6 \\ TSA=240unit^2 \end{gathered}[/tex]
Thus, the total surface area of the figure is 240 square units.
The volume formula is,
[tex]\begin{gathered} V=\frac{1}{2}lbh \\ V=\frac{1}{2}(6)(15)(3.2)\text{ \lbrack Since, A=}\frac{1}{2}bh\Rightarrow24=\frac{1}{2}(15)h\Rightarrow h=3.2] \\ V=144units^3 \end{gathered}[/tex]
Thus, the volume of the figure is 144 cubic units.
Final answer:
• The total surface area of the figure is 240 square units.
,
• The volume of the figure is 144 cubic units.
