Question

5 the area of $\triangle abc$ in the figure on the right is $24\\ \mathrm{cm}^2$. given point $d$ is the midpoint of side $ac$ and $be:ec = 1:2$, find the area of the triangles below.
(1) find the area of $\triangle bdc$.
\langle ans.\
angle
(2) find the area of $\triangle bde$.
\langle ans.\
angle
(3) find the area of $\triangle dec$.
\langle ans.\
angle
6 points per question

Explanation:

Step1: Find area of △BDC

D is midpoint of AC, so △BDC shares height with △ABC and base DC = ½ AC.
Area of △BDC = ½ × Area of △ABC = ½ × 24 = 12 cm².

Step2: Find area of △BDE

BE:EC = 1:2, so BE = ⅓ BC. △BDE shares height with △BDC and base BE = ⅓ BC.
Area of △BDE = ⅓ × Area of △BDC = ⅓ × 12 = 4 cm².

Step3: Find area of △DEC

△DEC shares height with △BDC and base EC = ⅔ BC.
Area of △DEC = ⅔ × Area of △BDC = ⅔ × 12 = 8 cm².

Answer:

12 cm²
4 cm²
8 cm²