Question

what is the area of this figure?
figure with dimensions: top length 9 km, right top segment 2 km, right bottom segment 4 km, bottom length 7 km, left side 6 km
box square kilometers
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Explanation:

Step1: Split the figure into two rectangles

We can split the T - shaped figure into a large rectangle and a small rectangle. The large rectangle has a length of \(7\) km and a height of \(6\) km. The small rectangle has a length of \(9 - 7=2\) km and a height of \(2\) km.

Step2: Calculate the area of the large rectangle

The area of a rectangle is given by the formula \(A = l\times h\), where \(l\) is the length and \(h\) is the height. For the large rectangle, \(l = 7\) km and \(h = 6\) km. So the area \(A_1=7\times6 = 42\) square kilometers.

Step3: Calculate the area of the small rectangle

For the small rectangle, \(l = 2\) km (since \(9 - 7 = 2\)) and \(h = 2\) km. Using the area formula for a rectangle, \(A_2=2\times2=4\) square kilometers.

Step4: Calculate the total area

The total area of the figure is the sum of the areas of the two rectangles. So \(A = A_1+A_2=42 + 4=46\) square kilometers.

Answer:

\(46\)