Question

1. select all the expressions that give the area of the figure in square units.

a. ((5 + 6) \times (3 + 2))
b. ((8 \times 6) - (3 \times 4))
c. (6 \times 8 \times 2 \times 3 \times 4 \times 5)
d. ((5 \times 6) + (3 \times 2))
e. (8 \times 6)

Explanation:

Step1: Analyze Option A

The figure is not a rectangle with length \(5 + 6\) and width \(3+2\), so \((5 + 6)\times(3 + 2)\) is incorrect.

Step2: Analyze Option B

The total area of a rectangle with length \(8\) and width \(6\) is \(8\times6\). The missing part is a rectangle with length \(3\) and width \(4\) (since \(6 - 2=4\) and \(8 - 5 = 3\)). So the area of the figure is \((8\times6)-(3\times4)\), which is correct.

Step3: Analyze Option C

Multiplying all those numbers is not a valid way to find the area, so this is incorrect.

Step4: Analyze Option D

The figure can be divided into two rectangles: one with length \(5\) and width \(6\), and another with length \(3\) and width \(2\). So the area is \((5\times6)+(3\times2)\), which is correct.

Step5: Analyze Option E

\(8\times6\) is the area of the larger rectangle, not the given figure, so this is incorrect.

Answer:

B. \((8\times6)-(3\times4)\), D. \((5\times6)+(3\times2)\)