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Which statement is always true?
A) Larger perimeter means larger area
B) Same perimeter means same area
C) Same base and height means same area (for triangles)
D) Area depends only on perimeter
B) Same perimeter means same area
C) Same base and height means same area (for triangles)
D) Area depends only on perimeter
- a)D
- b)C
- c)B
- d)A
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which statement is always true?A) Larger perimeter means larger areaB)...
Area of triangle = ½ × base × height
If base and height are same → area must be same.
If base and height are same → area must be same.
Community Answer
Which statement is always true?A) Larger perimeter means larger areaB)...
Understanding the Statements
To determine which statement is always true, let's analyze each option carefully.
A) Larger perimeter means larger area
- This statement is false. Different shapes can have the same perimeter but vastly different areas. For example, a long, thin rectangle can have the same perimeter as a compact square but will have a smaller area.
B) Same perimeter means same area
- This statement is also false. Different shapes can have the same perimeter but different areas. For instance, two different rectangles with the same perimeter can have varying lengths and widths, leading to differing areas.
C) Same base and height means same area (for triangles)
- This statement is true. For triangles, if the base and height are identical, the area will always be the same, regardless of the triangle's shape. The area of a triangle is calculated using the formula (1/2) * base * height.
D) Area depends only on perimeter
- This statement is false. Area is influenced by the dimensions of a shape and not solely by its perimeter. Two shapes can have the same perimeter but different areas, as previously mentioned.
Conclusion
Among the options provided, the correct and always true statement is:
- C) Same base and height means same area (for triangles)
This statement accurately reflects the fundamental property of triangles, ensuring consistency in area calculations based on these dimensions.
To determine which statement is always true, let's analyze each option carefully.
A) Larger perimeter means larger area
- This statement is false. Different shapes can have the same perimeter but vastly different areas. For example, a long, thin rectangle can have the same perimeter as a compact square but will have a smaller area.
B) Same perimeter means same area
- This statement is also false. Different shapes can have the same perimeter but different areas. For instance, two different rectangles with the same perimeter can have varying lengths and widths, leading to differing areas.
C) Same base and height means same area (for triangles)
- This statement is true. For triangles, if the base and height are identical, the area will always be the same, regardless of the triangle's shape. The area of a triangle is calculated using the formula (1/2) * base * height.
D) Area depends only on perimeter
- This statement is false. Area is influenced by the dimensions of a shape and not solely by its perimeter. Two shapes can have the same perimeter but different areas, as previously mentioned.
Conclusion
Among the options provided, the correct and always true statement is:
- C) Same base and height means same area (for triangles)
This statement accurately reflects the fundamental property of triangles, ensuring consistency in area calculations based on these dimensions.
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