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Answer:
52 units^2
Step-by-step explanation:
The area of the dresser is simple. It is just a rectangle that is 4 units by 3 units.
A_dresser = LW = 4(3) = 12 units^2
The area of the bed is a little more complicated, but you can get by using just areas of rectangles.
See the picture below.
Notice that the entire bed fits within a square (shown in blue) that is 9 units by 9 units.
The area of the square is 81 units^2.
We need to subtract the areas of the 4 triangles at the corners.
There are two triangles, top left and bottom right (shown in green), that have a base of 5 and a height of 5. They combine to for a square that is 5 units by 5 units. The area of this square is 25 units^2.
There are two triangles, top right and bottom left (shown in red), that have a base of 4 and a height of 4. They combine to for a square that is 4 units by 4 units. The area of this square is 16 units^2.
Now subtract 25 and 16 from 81 to get the area of the bed.
81 - 25 - 16 = 40
A_bed = 40 units^2
Combined area of bed and dresser:
A = 40 units^2 + 12 units^2 = 52 units^2
Answer: 52 units^2
Here's another way of finding the area of the bed:
Count the number of full squares inside the bed (there are 31). Each full square is 1 unit^2. Then count the number of half-squares inside the bed (there are 18). Each half-square is 1/2 units^2. Add them all up:
31 + 1/2 * 18 = 31 + 9 = 40
You get 40 units^2
