A square and a rectangle have the same perimeter of 36 cm. Which quadrangle is larger if the rectangle is 10 cm long?

| January 22, 2021 | education

We need to determine which quadrangle has a larger area. To do this, consider each quadrangle separately.

Square:

Formula for calculating the perimeter:

P = 4 * a

Where a is the edge length of the square.

From the problem statement, we know that P = 36 centimeters.

Then:

4 * a = 36
a = 36/4
a = 9 centimeters

Knowing the length of the edge, we can find the area of ​​the square:

Sq = a ^ 2 = 9 ^ 2 = 81 cm sq.

Rectangle:

The perimeter of the rectangle is calculated using the formula:

P = 2 * (a + b)

Where a is the length,
b – width.

From the condition we know that a = 10 cm and P = 36 cm.Then:

2 * (a + b) = 36
2 * a + 2 * b = 36
2 * 10 + 2 * b = 36
20 + 2 * b = 36
2 * b = 16
b = 8 cm

Rectangle area:

Spr = a * b = 10 * 8 = 80 cm sq.

You can see that the area of ​​the square is larger



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