The triangle in the rectangle
✓ With solution
A rectangle, a shaded triangle and a point that can slide. What is the triangle's area?
A rectangle is 10 cm long and 6 cm tall. We pick a point P anywhere on its top side and join it to the two bottom corners, which makes the shaded triangle in the picture.
What is the area of the shaded triangle?
- A24 cm²
- B30 cm²
- C36 cm²
- DIt depends where P is
Show the answer
Answer: B) 30 cm². Draw a straight line from P down to the base. It splits the rectangle into two rectangles, and each slanted side of the triangle is a diagonal of one of them; a diagonal cuts a rectangle into two equal halves. So the shaded triangle takes half of each small rectangle, which is half the big one: 10 × 6 ÷ 2 = 30 cm², wherever P is. Another way: a triangle's area is base × height ÷ 2, and the base is always 10 and the height always 6, however P moves.
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