question_answer 31)

Split the following shapes into rectangles and find their areas (The measures are given in centimeters).                

Answer:

                (a)  the given Let divided into two rectangles A, B and their length and breadth are written on the figure. For rectangle A,                          Length = 12 cm and breadth = 2 cm            \[\therefore \]Area of the rectangle A = Length \[\times \] Breadth   = 12 cm \[\times \] 2 cm =.24 sq cm         For rectangle B,                      Length = 8 cm and breadth = 2cm     \[\therefore \] Area of the rectangle B = Length\[\therefore \]x Breadth \[\text{= 8cm}\times \text{2cm}\,\text{=16sqcm}\] Now, total area of given figure = Area of rectangle A + Area of rectangle B = (24 +16) sq cm = 40 sq cm Hence, required area is 40 sq cm. (b) Let the given figure is divided into 5 squares and their length are written on the figure Side of the one square = 7 cm \[\therefore \]Area of the one square \[\text{= Side}\times \text{Side =7cm}\times \text{7cm = 49 sq cm}\] Since, all squares have equal sides i.e. 7 cm.   So, all five square have same area i.e. 49 sq cm Now, total area of given figure 5 x Area of one square  \[=(5\times 49)sqcm=245sqcm\]      Hence, required area is 245 sq cm.  (c) Let the given figure is divided into rectangles A, B and their length and breadth are written on the figure. For rectangle A,                              Length = 5 cm and breadth = 1 cm              \[\therefore \]Area of the rectangle A = Length \[\times \]Breadth \[=5\times 1cm=5sqcm\]        For rectangle B,                                      Length = 4 cm and breadth = 1 cm \[\therefore \]Area of the rectangle B = Length \[\times \] Breadth \[=4cm\times 1cm=4sqcm\] Now, area of given figure = Area of rectangle A + Area of rectangle B\[=(5+4)sqcm=9sqcm\] Hence, the area of the given figure is 9 sq cm.