Area of the sector?
A hard-level "Area" problem."Arc × radius ÷ 2" works without knowing the central angle. Apply it to a whole circle, where the arc is the circumference, and the formula for a circle's area drops straight out.
GivenRadius 12 cm, arc length 10 cm. The central angle is not given
Hints
- The central angle is unknown, so "such-and-such a fraction of a circle" is closed to us. We need a route that uses only the arc length and the radius.
- Slice the sector into 8 thin wedges, like a pizza. Each slice is a long thin isosceles triangle.
- Move the slices over to the right and lay them out alternately pointing up and down. Cutting and rearranging changes nothing, so the area is untouched.
- Look at the width of the new shape. The arc has been shared out half along the top and half along the bottom, so the width is 10 ÷ 2 = 5 cm.
- The height is the height of each slice — that is, the radius, 12 cm.
- The finer the slices, the more the zigzag vanishes and the closer it comes to a true rectangle. So the area is 5 × 12 — in short, "arc × radius ÷ 2".
Answer 60cm²
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?