# Mensuration-31

### From Homeworkwiki

**From a piece of cardboard, in the shape of a trapezium ABCD, and AB || DC an angle BCD = 90 ^{0},**

**quarter circle is removed.**

**Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the cardboard.**

**Solution:** AB = 3.5 cm, EC = 3.5 cm, DC = 2 cm + 3.5 cm = 5.5 cm

Area of the trapezium ABCD = 1/2 (AB + DC) x BC = 1/2 (3.5 + 5.5) x 3.5 cm^{2}

= 1/2 x 9 x 3.5 cm^{2} = 15.75 cm^{2}

Area of the quarter circle BFEC = 1/4 x Π x 3.5^{2}

= 1/4 x 22/7 x 3.5 x 3.5 = 9.625 cm^{2}

Therefore, Area of the remaining piece of the cardboard = (15.75 - 9.625) cm^{2} = 6.125 cm^{2}