Area of the inner triangle?
A hard-level "Area" problem.Divide all three sides in the same ratio and the middle triangle is always a fixed fraction of the whole — 21/63 here — regardless of the triangle's shape.
GivenTriangle ABC has area 63 cm². All three sides are divided 1 : 2
Hints
- There is no way to get the middle triangle directly. The only route is to work out the three corners and subtract them from the whole.
- Take one corner, triangle ADF. AD is 1/3 of AB and AF is 2/3 of AC. As before, multiply the two ratios.
- 63 × 1/3 × 2/3 = 14 cm² for one corner.
- Here is the satisfying part: all three corners are built from the same pair of ratios (1/3 and 2/3). Only their orientation differs — the areas are identical.
- Three of them: 14 × 3 = 42 cm². Subtract from the whole: 63 − 42
Answer 21cm²
More "Area" problems
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?
- What area of the table is covered by paper?