Answer:
57 cm²
Step-by-step explanation:
You have a composite figure and you want to find its area.
Decomposition
There are several ways you can decompose the given figure. Three of them are shown in the attachments. The missing dimensions are found by realizing that the sum of the right-side dimensions is equal to the left-side dimension, and the sum of the bottom-side dimensions is equal to the top dimension.
Extend the vertical line
Extending the vertical boundary line divides the figure into a left rectangle that is 7 cm high and 7 cm wide, and a right rectangle that is 2 cm high and 4 cm wide. This is shown in the first attachment.
The area of each rectangle is the product of its height and width, and the total area is the sum of these:
Area = (height)×(width) . . . . . area formula for one rectangle
Area = (7 cm)(7 cm) +(2 cm)(4 cm) = 49 cm² +8 cm² = 57 cm²
Extend the horizontal line
Extending the horizontal boundary line divides the figure into a top rectangle 2 cm high and 11 cm wide, and a bottom rectangle 5 cm high and 7 cm wide. This is shown in the second attachment. The total area is ...
Area = (2 cm)(11 cm) +(5 cm)(7 cm) = 22 cm² +35 cm² = 57 cm²
Draw a diagonal line
A line can be drawn corner-to-corner to divide the figure into two trapezoids. This is shown in the third attachment.
The upper right trapezoid has bases 11 cm and 4 cm, and height 2 cm.
The lower left trapezoid has bases 7 cm and 5 cm, and height 7 cm.
The area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
Then the total area is ...
Area = 1/2(11 cm +4 cm)(2 cm) +1/2(7 cm +5 cm)(7 cm) = 15 cm² +42 cm²
Area = 57 cm²
Subtract the negative area
The rectangle that encloses the entire figure is 7 cm high and 11 cm wide, so has an area of ...
A = HW = (7 cm)(11 cm) = 77 cm²
From that area, the lower right corner space is cut out. It has dimensions 5 cm high by 4 cm wide, so an area of (5 cm)(4 cm) = 20 cm².
The area of the figure itself is the difference between the area of the bounding rectangle and the area of the cut-out space at lower right:
Area = 77 cm² -20 cm² = 57 cm²
The area of the figure in the picture is 57 cm².
