Area of this triangle?
A normal-level "Area" problem."Sliding a vertex along a parallel line does not change the area" — this is shearing. It is the tool for turning an awkward shape into a manageable one.
GivenBase 12 cm / height 8 cm
Hints
- A triangle's area is "base × height ÷ 2". The base is BC = 12 cm.
- The height is the perpendicular distance from A down to the base line (extended): 8 cm. It is not the length of the slanted side AB. This is where most people slip.
- Now draw the line ℓ through A, parallel to the base BC. Vertex A sits on this line.
- Slide vertex A along ℓ. Even when it moves right above B, the gap between ℓ and BC never changes, so the height stays the same — and the base BC has not moved either.
- Clear the working lines and look at the new triangle alone: an upright triangle with base 12 cm and height 8 cm. Its area is the same as the original.
- Now just the formula: 12 × 8 ÷ 2
Answer 48cm²
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?