Area of triangle ADE?
A hard-level "Area" problem.Know the ratios on two sides and the triangle between them is just two multiplications. Almost every area-ratio problem can be forced into this shape.
GivenTriangle ABC has area 60 cm². AD : DB = 2 : 1, AE : EC = 3 : 2
Hints
- Triangle ADE is ABC trimmed in two places at once. You cannot do both in one go, so take it in two steps, going via triangle ADC.
- Step one: compare triangle ADC with triangle ABC. Both have apex C, and their bases AD and AB lie on the same line — so they have the same height.
- Same height means area follows the base. AD : AB = 2 : 3, so triangle ADC = 60 × 2 ÷ 3 = 40 cm².
- Step two: triangle ADE against triangle ADC. Both have apex D, and their bases AE and AC lie on the same line — same height again, for exactly the same reason.
- AE : AC = 3 : 5, so the answer is 40 × 3 ÷ 5.
- In short, you just multiply the two ratios in turn. As long as you keep track of which apex was shared at each step, there is nothing to get lost in.
Answer 24cm²
More "Area" problems
- Area of the inner triangle?
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?