use a 15 cm long string and join its ends. place it on cm squared paper to make a square ,a circle, a triangle, and a rectangle. find the area of each shape .which shape has the largest area ?which shape ha a smallest area?
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The shapes with largest area and shape with smallest area are circle and triangle.
Step-by-step explanation:
Length of the string = 15 cm
Thus, perimeter = 15 cm
Square:
A square has four sides.
One side:
a = 15/4 = 3.75 cm
Area:
As = a² = (3.75)² = 14.06 cm²
Circle:
Circumference:
C = 2πR
15 = 2πR
∴ R = 15/2π
Area:
Ac = πR² = π(15/2π)²
Ac = 17.9 cm²
Triangle:
A triangle has three sides. Since, many triangles are formed with this measurement. Equilateral triangle is considered.
Side:
a = 15/3 = 5 cm
Area:
At = (√3 /4) a²
At = (√3 /4)5² = 10.8 cm²
Rectangle:
Since, many rectangles can be formed with given string. One of the value is mentioned below.
When l = 7 cm and w = 0.5 cm, the area is:
Ar = 7 × 0.5 = 3.5 cm²
Conclusion:
Ac > As > At > Ar
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2
Answer is also make triangle .square.rectangle and circle
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