Question

what is the area of this figure? 95mm² 4mm 6mm 3mm 5mm 9mm 7mm 4mm 2mm

Explanation:

Step1: Divide the figure into simple shapes

Divide the figure into a trapezoid, a rectangle, and another rectangle.

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 4\) mm, \(b=9\) mm, and \(h = 6\) mm.

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Step3: Calculate the area of the first rectangle

The formula for the area of a rectangle is \(A = lw\), where \(l=9\) mm and \(w = 2\) mm.

$$A_{2}=9\times2=18\text{ mm}^2$$

Step4: Calculate the area of the second rectangle

First, find the length of the second rectangle. The total length of the base of the figure: \(6+2 + 7+3=18\) mm. The height of the second rectangle: \(4 + 5=9\) mm. But we can also calculate it as follows. The length is \(7 + 3=10\) mm and the height is \(5\) mm, and there is another part with length \(7\) mm and height \(4\) mm.

$$A_{3}=(7 + 3)\times5+7\times4=50 + 28=78\text{ mm}^2$$

Step5: Sum up the areas of all shapes

$$A=A_{1}+A_{2}+A_{3}=39+18 + 78=95\text{ mm}^2$$

Answer:

\(95\) mm²