To solve the problem, we need to clarify the given dimensions and understand the configuration of the shapes involved. However, the description seems a bit ambiguous since areas are usually expressed in square units, while lengths are in linear units. Let's work through this step by step.
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Understanding the Triangle: It sounds like you have a triangle (shape b) whose "outer sides" are specified as 9 m and 16 m. Since we are dealing with lengths, I will assume you meant that two sides of the triangle measure 9 m and 16 m.
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Finding the Third Side and Area of the Triangle: To find the area of the triangle, we also need the length of the third side or an angle between the two known sides. If we assume it is a right triangle, where the sides of 9 m and 16 m are perpendicular, we can calculate the area as:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 16 = 72 \text{ m}^2. \]
If the triangle is not a right triangle, we'll need more information (such as an angle or the length of the third side) to calculate its area using Heron's formula or the sine area formula.
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Area of the Square (Shape a): The area of the square is typically calculated using the length of one side squared. If you want the area of the square, we need its side length (which we currently do not have).
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Finding the Length of Shape b: If we consider only the triangle, we can calculate the perimeter (the sum of all three sides). The lengths of the two known sides are 9 m and 16 m, and we still need the length of the third side.
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Conclusion and Required Information: To provide the complete answer, I need clarification on:
- Whether the triangle is right-angled or not. If not, please provide more information about the triangle (e.g., the length of the third side or an angle).
- The side length of the square (shape a).
If you can provide that additional information, I would be glad to help you find the areas and lengths you're asking for!