⁦Area of a rhombus and a circle⁩

⁦The diagonals of a⁩ معين ⁦are perpendicular and cut each other in half⁩. ⁦They divide the rhombus into 4 equal right-angled triangles⁩. ⁦If the diagonals are 8 and 6, the legs of each triangle are 4 and 3⁩.

⁦If we draw a rectangle round the rhombus whose sides equal the two diagonals, the rectangle is made of the rhombus and 4 triangles equal to the 4 inside it⁩. ⁦So the area of the rhombus is half the area of the rectangle⁩.

⁦So the area of a rhombus equals the product of the two diagonals divided by 2⁩. ⁦A common mistake is to forget the ÷ 2 or to add the diagonals⁩.

⁦If we cut a circle into equal sectors and lay them side by side, the shape is close to a⁩ متوازي الأضلاع ⁦whose base is half the⁩ محيط الدائرة ⁦and whose height is the⁩ نصف قطر. ⁦So area of a circle = half the circumference × radius⁩.

⁦Because the circumference is ٢×٣٫١٤×r, half of it is ٣٫١٤×r⁩. ⁦So the area of a circle is pi × radius × radius, with ٣٫١٤ for pi⁩. ⁦If you have the diameter, halve it first⁩.