question_answer

       

(a) If ABCD is a square of side 14 cm and APB and DPC are semi-circles, then find the area of shaded region as shown in the figure.

(b) If area of a trapezium is 44 cm2, whose parallel sides are 10 cm and 12 cm and height is 4 cm, then verify that Area of trapezium \[=\frac{1}{2}\] [sum of parallel sides] \[\times \]height.

Answer:

(a) Area of the shaded region = Area of square ABCD - Area of 2 semi circles                                  1

\[={{14}^{2}}-2\times \frac{1}{2}\times \pi \times {{7}^{2}}\]

\[=14\times 14-\frac{22}{7}\times 7\times 7\]

\[=\left( 196154 \right)=42\text{ }c{{m}^{2}}\]

(b) Since, area of a trapezium \[=\text{ }44\text{ }c{{m}^{2}}\]

Parallel sides = 10 cm and 12 cm

and            h = 4 cm

Then, L.H.S. \[=\text{ }44\text{ }c{{m}^{2}}\]

Area of trapezium \[=\frac{1}{2}\times \](sum of parallel sides) \[\times \] height

and            R.H.S. \[=\frac{1}{2}\times (10+12)\times 4\]

\[=\frac{1}{2}\times \text{ }22\text{ }\times \text{ }4\]

\[=\text{ }44\text{ }c{{m}^{2}}\]

Hence, L.H.S. = R.H.S. \[=\text{ }44\text{ }c{{m}^{2}}\]