Question

Can I please have some help.?

Answer 1

check the picture below.

we know the perimeter is 28, the values we know are 4, 2 and 3.

the right-side of the figure, is just 4 + 2, therefore 6.

the bottom-right side of the figure, is just a mirror length of above, therefore 3.

the other two lengths, are twins, and since if we pluck out the values from the perimeter, we have

28 - 4 - 2 - 3 - 6 - 3 = 20.

since the last two lengths are twins, then each one is 20/10 or 10, as you see there in the picture.

now, we can get the full are of the figure, because is just two rectangles, as you see there, so the area is just

(4*10) + (3*6), namely 58.

notice, the figure there, has two triangles.

one on the left-hand-side, has a base of (10+3) and a height of 4.

the other triangle on the right-hand-side has a base of 3, and a height of 6.

we can just get the area of both triangles, and then subtract them from the total area of the figure, what's leftover, is the shaded section.

$\bf \stackrel{\textit{total area}}{58}~~-~~\stackrel{\textit{left triangle area}}{\cfrac{1}{2}(13)(4)}~~-~~\stackrel{\textit{right triangle area}}{\cfrac{1}{2}(3)(6)} \\\\\\ 58~~-~~26~~-~~9\implies \boxed{23}$