How to find a parallelogram on a coordinate plane

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SSAT Middle Level Quantitative › How to find a parallelogram on a coordinate plane

Questions 1 - 4

Triangle5

Given a base of 12 units and an area of 120 square units, find the height of the paralellogram shown above.

$\sqrt{10}$

Explanation

The area formula for a parallelogram is:

$A = base \times height$

Thus, to find the height, rearrange:

$height = \frac{A}{base} = \frac{120}{12} = 10$

Parellelogram

NOTE: Figure NOT drawn to scale.

What is the area of the parallelogram represented by the above figure?

Explanation

The area of a parallelogram is its base multiplied by its height. The diagram below shows both in green:

Parellelogram

$A = 9 \cdot5 = 45$

Triangle5

Find the area of the above parallelogram given a height of 5 units, as shown to scale.

$30 \text{ square units}$

$25 \text{ square units}$

$15 \text{ square units}$

$12.5 \text{ square units}$

Explanation

Since the diagram is drawn to scale, the base of the parallelogram must be 6 units in length. Using the area formula for a parallelogram:

$A = base \times height = 6 \times 5 = 30$

Triangle5

The above parallelogram has an area of 30 square units. Which of the following could be the lengths of the base and height of this figure? (Image not drawn to scale.)

Explanation

The formula for the area of a parallelogram is:

$A = base \times height$

Thus, the base and height must equal 30 square units when multiplied together.

3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units.

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