Answer:
80 cm²
Step-by-step explanation:
Trapezoid LPKB has area ...
A = (1/2)(b1 +b2)h = (1/2)(4 +20)(20) = 240 . . . . cm²
Triangle BPN has area ...
A = (1/2)bh = (1/2)(20)(20) = 200 . . . . cm²
Triangle BKN has a height that is 4/5 the height of triangle BPN, so will have 4/5 the area:
ΔBKN = (4/5)(200 cm²) = 160 cm²
The area of quadrilateral LPKB is that of trapezoid LPNB less the area of triangle BKN, so is ...
240 cm² - 160 cm² = 80 cm²
