Answer:
(a) 58 m²
Step-by-step explanation:
The area of a composite figure is found by dividing it into simpler shapes whose area formulas are known.
Division
Extending the horizontal line to the left, we find it divides the shape into an upper rectangle with dimensions 2 m wide and 4 m high, and a lower rectangle with dimensions 10 m wide and 5 m high.
Rectangle area
The area of a rectangle is the product of its dimensions:
A = LW . . . . . where L is the length and W is the width
The upper rectangle has an area of ...
A = (4 m)(2 m) = 8 m²
The lower rectangle has an area of ...
A = (10 m)(5 m) = 50 m²
Total area
The area of the figure is the sum of the areas of the upper and lower rectangles:
A = (8 m²) +(50 m²) = 58 m²
The area of the figure is 58 square meters.
Additional comment
The area can also be figured by considering an enclosing rectangle 9 m high by 10 m wide, for an area of (9 m)(10 m) = 90 m². From this rectangle, a rectangle 4 m high and 8 m wide is removed from the upper right corner. The removed area is (4 m)(8 m) = 32 m². Then the remaining area is ...
90 m² -32 m² = 58 m² . . . . the area of the figure shown
