Answer:
Once the height of the figures are the same and the total height is 24, each one height is 6.
Note: I wil consider square metre as the unit of area.
First, I will calculate the half-length of the triangle base using the pythagorean theorem:
[tex]10^{2}=6^2+x^2\\ 100=36+x^2\\64=x^2\\x=8m[/tex]
∴The base is equal to 16m
Let's calculate the area of the triangle:
[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2} (16)(6)\\\\A=\frac{1}{2} (16)(6)= 48m^2[/tex]
Now, let's calculate the first rectangle Area:
[tex]A=wh\\A=(16)(6)\\A=96m^2[/tex]
Now, the trapezoid area:
The width length of the longer side is equal to 16 plus the length of 2 little triangles. Those triangles base length equal to half-length of the first triangle. Therefore, the longer side/base is equal to 32.
[tex]A=\frac{1}{2} (longerSide+shorterSide)height\\A=\frac{1}{2} (32+16)6\\A=144m^2[/tex]
Now, the last rectangle:
[tex]A=wh\\A=(32)(6)\\A=192m^2[/tex]
Therefore, the figure Total Area is the sum of the triangle, trapezoid and rectangles:
[tex]48+96+144+192=480m^2[/tex]
A = 480 unit of area
