1 Answer

Cralfaro · Answer 1 · 2023-12-17T19:48:09+0000

Question:

Solution:

The given figure is composed of the following figures:

1) two lower triangles and a square.

2) An upper triangle. (the biggest)

Therefore, the area of the given figure is the sum of the figures that compose it. Now, from now on, let us denote the height by h and the base by b.

Lower triangles:

Area of the lower-left triangle:

$ALT\text{ =}\frac{b\text{ x h}}{2}\text{ = }((2)(2))/(2)=\text{ 2}$

Area of the lower-right triangle:

$ART\text{ =}\frac{b\text{ x h}}{2}\text{ = }((5)(2))/(2)=5$

Area of the lower square:

$AS\text{ = bxh = (2)(2) = 4}$

Upper triangle:

Area of the upper triangle:

$AUT\text{ =}\frac{b\text{ x h}}{2}\text{ = }((9)(3.5))/(2)=15.75$

Thus, we can conclude that the total area of the shape shown is:

$A\text{ = ALT + ART + AS+ AUT }$

that is:

$A\text{ =}2+5+4+15.75\text{ = 26.75}$

Then, the correct answer is:

$A\text{ = 26.75}$