Question

Lots of points plz help

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Answer 1

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:

`10^(2)=6^2+x^2\\ 100=36+x^2\\64=x^2\\x=8m`

∴The base is equal to 16m

Let's calculate the area of the triangle:

`A=(1)/(2) bh\\\\A=(1)/(2) (16)(6)\\\\A=(1)/(2) (16)(6)= 48m^2`

Now, let's calculate the first rectangle Area:

`A=wh\\A=(16)(6)\\A=96m^2`

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.

`A=(1)/(2) (longerSide+shorterSide)height\\A=(1)/(2) (32+16)6\\A=144m^2`

Now, the last rectangle:

`A=wh\\A=(32)(6)\\A=192m^2`

Therefore, the figure Total Area is the sum of the triangle, trapezoid and rectangles:

`48+96+144+192=480m^2`

A = 480 unit of area

Answer 2

= 480 u2

Explanation:

=

1

2 bh + bh +

1

2 (b1 + b2)h + bh

=

1

2 (16)(6) + (16)(6) +

1

2 (16 + 32)(6) + (32)(6)

= 48 + 96 + 144 + 192