Question

what is the area of this figure?
3 cm
2 cm
5 cm
9 cm
7 cm
8 cm
square centimeters
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Explanation:

Step1: Divide the figure into two rectangles

We can split the L - shaped figure into a smaller rectangle (top - left) and a larger rectangle (bottom - right). The smaller rectangle has a width of 3 cm and a height of 2 cm. The larger rectangle has a width of 8 cm and a height of 7 cm.

Step2: Calculate the area of the smaller rectangle

The formula for the area of a rectangle is \(A = l\times w\) (where \(l\) is length and \(w\) is width). For the smaller rectangle, \(l = 3\space cm\) and \(w=2\space cm\), so its area \(A_1=3\times2 = 6\space cm^2\).

Step3: Calculate the area of the larger rectangle

For the larger rectangle, \(l = 8\space cm\) and \(w = 7\space cm\), so its area \(A_2=8\times7=56\space cm^2\).

Step4: Calculate the total area

The total area of the figure is the sum of the areas of the two rectangles. So \(A = A_1+A_2=6 + 56=62\space cm^2\). (Alternative way: We can also consider the figure as a big rectangle of \(8\times9\) minus a rectangle of \(5\times(9 - 7)\). Let's verify: \(8\times9=72\), \(5\times(9 - 7)=5\times2 = 10\), \(72-10 = 62\). Same result.)

Answer:

62