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3 years ago

How many properties of parallelograms are there?

Mathematics

1 answer:

Ludmilka [50]3 years ago

5 0

Answer: The answer is six.

Step-by-step explanation: There are six important properties of a parallelogram. Please see the attached figure. The properties are as follows :

(i) The opposite sides of a parallelogram are parallel and congruent, i.e., PQ║RS, QR║PS, PQ ≅ RS and QR ≅ PS.

(ii) The opposite angles of a parallelogram are congruent, i.e., ∠P = ∠R and ∠Q = ∠S.

(iii) The diagonals of a parallelogram bisect each other, i.e., OP = OR and OQ = OS.

(iv) Consecutive angles of a parallelogram are supplementary. For example, ∠P + ∠Q = 180°.

(v) If one angles of a parallelogram is 90°, then all the angles are 90°.

(vi) Each diagonal of a parallelogram separates it into two congruent triangles. For example, ΔPQR ≅ ΔSQR.

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16 times larger is the new area when compared to the original.

Given that, the length of each side of the square is quadrupled.

We need to find how many times larger is the new area when compared to the original.

<h3>What is the area of a square?</h3>

A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the area of the square. The formula to calculate the area of a square is a².

Let the length of each side of the square be x.

Then the length of each side of the new square will be 4x.

Now, the area of the original square = x²

The area of the new square = (4x)² = 16x²

So, the new square = 16 × the original square

Therefore, 16 times larger is the new area when compared to the original.

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