question_answer 44)

Find the area of the quadrilateral ABCD.                                    Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and \[\text{BM}\bot \text{AC,DN}\bot \text{AC}\].

Answer:

                Area of the quadrilateral ABCD = Area of the triangle ABC + Area of the triangle ADC                           \[\text{= }\frac{\text{1}}{\text{2}}\text{(base  }\!\!\times\!\!\text{  height) + }\frac{\text{1}}{\text{2}}\text{(base  }\!\!\times\!\!\text{  height)}\]                 \[=\frac{1}{2}(22\times 3\text{) c}{{\text{m}}^{\text{2}}}+\frac{1}{2}(22\times 3\text{) c}{{\text{m}}^{\text{2}}}\]                 \[\text{= 33 c}{{\text{m}}^{\text{2}}}\text{+ 33 c}{{\text{m}}^{\text{2}}}\text{= 66 c}{{\text{m}}^{\text{2}}}\]