Explanation:
there are two side lengths missing : the top vertical side between (2p - 1) and (p - 1). let's call it x. and the lower middle horizontal side between (p + 1) and p. let's call it y.
we see that the long vertical side in the right covering all 3 sub-rectangles is (4p - 2).
on the left side we have as vertical sides p and (p + 1) and then our missing side. all 3 together must be the same as (4p - 2) :
4p - 2 = p + (p + 1) + x = 2p + 1 + x
x = 2p - 3
and we see that the total horizontal length of the object is
(2p - 1) + (p - 1) = 3p - 2
and that must be the same as the total horizontal length on the lower side
3p - 2 = (p + 3) + y
y = 2p - 5
(i)
the perimeter is then
(4p-2) + (p+3) + p + (2p-5) + (p+1) + (2p-1) + (2p-3) + (p-1) =
= 14p -8
(ii)
the area is the sum of the 3 sub-rectangles :
(p-1)(2p-3)
(p+1)((2p-1) + (p-1)) = (p+1)(3p-2)
p(p+3)
(p-1)(2p-3) = 2p² - 3p - 2p + 3 = 2p² - 5p + 3
(p+1)(3p-2) = 3p² - 2p + 3p - 2 = 3p² + p - 2
p(p+3) = p² + 3p
the sum of these 3 terms is the total area
2p² - 5p + 3 + 3p² + p - 2 + p² + 3p =
= 6p² - p + 1