2018 · Q98
In the equilateral triangle ABC given below, AD = DB and AE = EC. If l is the length of a side of the triangle, then what is the area of the shaded region?
Elementary MathematicsMensuration
- A3√3l²/16
- B3l²/16
- C3√3l²/32
- D3l²/32
Explanation
D and E are midpoints, so △ADE ~ △ABC with linear ratio 1/2 and area ratio 1/4: area(ADE) = (√3/16)l². The shaded trapezium DBCE is the remainder: (√3/4)l² − (√3/16)l² = 3√3l²/16, option (A).