Math Problem Statement
What is the area of this figure?
Solution
The figure you uploaded is a compound shape, and the task is to find the area. To do this, we can break the figure into simpler rectangles and find the area of each, then sum the areas.
Step-by-Step Breakdown:
-
Left Rectangle:
- Width: 11 mi
- Height: 4 mi
- Area =
-
Top Rectangle:
- Width: 9 mi
- Height: 3 mi
- Area =
-
Bottom Right Rectangle:
- Width: 6 mi (from the height of 11 mi minus the top 3 mi and the small bottom rectangles of 2 mi and 3 mi)
- Height: 2 mi
- Area =
-
Small Bottom Rectangle:
- Width: 3 mi
- Height: 2 mi
- Area =
-
Far Right Rectangle:
- Width: 2 mi
- Height: 6 mi
- Area =
Total Area:
Adding up all the areas:
So, the total area of the figure is 101 square miles.
Would you like more details or have any further questions?
Here are 5 related questions:
- How would the area change if the top rectangle's width increased by 2 miles?
- Can you break down this compound figure in a different way to verify the area?
- How does breaking down a complex figure into simpler shapes make calculations easier?
- What would the area be if the entire figure were shifted horizontally by 5 miles?
- Can you use the same method to find the perimeter of this compound figure?
Tip: Always ensure the dimensions of smaller rectangles add up correctly to match the overall shape!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Area of compound figures
Rectangles
Formulas
Area of a rectangle = width × height
Theorems
Additive property of areas
Suitable Grade Level
Grade 6