Question

The total surface area of each figurefigure iv find surface area and volume

Answer 1

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.

Step-by-step explanation:

The total surface area of the figure is,

Using the heron's formula,

`\begin{gathered} S=(a+b+c)/(2) \\ =(4+13+15)/(2) \\ =(32)/(2) \\ s=16 \end{gathered}`

The area of the triangle will be,

`\begin{gathered} A=√(s(s-a)(s-b)(s-c)) \\ A=√(16(16-4)(16-13)(16-15)) \\ A=24unit^2 \end{gathered}`

Therefore, the total surface area of the figure becomes,

`\begin{gathered} TSA=2*24+4*6+13*6+15*6 \\ TSA=240unit^2 \end{gathered}`

Thus, the total surface area of the figure is 240 square units.

The volume formula is,

`\begin{gathered} V=(1)/(2)lbh \\ V=(1)/(2)(6)(15)(3.2)\text{ \lbrack Since, A=}(1)/(2)bh\Rightarrow24=(1)/(2)(15)h\Rightarrow h=3.2] \\ V=144units^3 \end{gathered}`

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.