Question

Given: LMNB is a square, LM = 20cm, P∈ LM , K ∈ PN , PK = 1 5 PN, LP = 4 cm Find: Area of LPKB

Answer 1

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