Question

A parallelogram with a base of y units and a height of x units is changed to have a new base of 3y units and a height of 2x units, as shown in the figures below. if the area of the original parallelogram is 47 square units, determine the area of the new parallelogram.

Answer 1

The formula for the area of a parallelogram is

A=b*h    where b=base and h=height

if the base were to increase by 3times and the height were to increase by 2 times then
6A=b*h
The area of the parallelogram would be 6 times larger

So if the original area was 47units², then the new area would be

47*6=282units²

Answer=282units²

Answer 2

The area of the new parallelogram for the given condition is evaluated being of 282 sq. units.

How to find the area of a parallelogram whose height and base length are given?

Suppose the considered parallelogram has:

• height  = h units
• length of base = b units.

Then, we get:

$A = b \times h \: \rm unit^2$ (as area of the parallelogram).

For this case, we are specified that:

The old parallelogram had base of y units and height of x units.

Its area was 47 sq. units.

That means:

$A = xy = 47$

Now, new parallelogram has base of 3y units and height of 2x units.

Its area would be:

$A = 3x \times 2y = 6xy = 6 \times xy = 6 \times 47 = 282 \: \rm unit^2$ (because we had $xy = 47$)

(sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together. Thus, $xy = x \times y$)

Thus, the area of the new parallelogram for the given condition is evaluated being of 282 sq. units.

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