Question

(AMC8, 2000) The area of rectangle ABCD is 72. If point A and the midpoints of BC and CD are joined to form triangle, the area of that triangle is: A: 21, B: 27, C: 30, D: 36, E: 40

Its a multiple choice question

Answer 1

B: 27

Explanation:

See the attached diagram.

Here, area of Δ AEF = area of ABCD - area of Δ ABE - area of Δ ADF - area of Δ ECF

⇒ area of Δ AEF =
`WL - (1)/(2) * L * (W)/(2) - (1)/(2) * W* (L)/(2) - (1)/(2) * (L)/(2) * (W)/(2)`

=
`WL - (WL)/(4) - (WL)/(4) - (WL)/(8)`

=
`(3WL)/(8)`

=
`(3)/(8)* (72)` {Since the area of the rectangle WL is given to be 72}

= 27 (Answer)