Understand the Problem
The question involves a geometric figure with specific markings and dimensions. It seems to relate to calculating or understanding the properties of the shape, possibly in the context of angles or areas within a polygon.
Answer
The area of the diamond shape is $50a^2$.
Answer for screen readers
The area of the diamond shape is $50a^2$.
Steps to Solve
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Identify the dimensions of the shape
The given figure is a diamond shape with the corners marked. The lengths of the segments are as follows:
- Each outer segment (EF, EH, HG, GF) measures $6a$.
- The inner segments (AB, BC, CD, DA) are marked as $2a$.
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Calculate the total vertical and horizontal dimensions of the diamond
Since the diamond is made up of a square in the center and equal lengths extending from its corners, the total height and width can be calculated as follows:
For the vertical dimension: $$ \text{Total height} = 6a + 2a + 2a = 10a $$
For the horizontal dimension: $$ \text{Total width} = 6a + 2a + 2a = 10a $$
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Calculate the area of the diamond shape
The area of a diamond (or rhombus) can be found using the formula: $$ \text{Area} = \frac{1}{2} \times d_1 \times d_2 $$ where $d_1$ and $d_2$ are the lengths of the diagonals. In this case, both diagonals are equal to the total vertical and horizontal dimensions calculated earlier.
For our diamond: $$ \text{Area} = \frac{1}{2} \times 10a \times 10a = 50a^2 $$
The area of the diamond shape is $50a^2$.
More Information
This geometric figure showcases a diamond (or rhombus) made from a central square and segments extending from each corner. The calculations involve basic principles of geometry, specifically understanding how to find area using diagonals.
Tips
- Forgetting to account for both diagonals: Since the diamond has equal dimensions on both axes, sometimes they can be mistaken as different lengths.
- Misreading dimensions: Always double-check the measurements labeled on the shape to avoid errors in calculations.
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