Question

How do I find the area of a parallelogram on the coordinate plane? the vertices of this parallelogram are A (-4, -3) B (2, -3) C (4, -6) D (-2, -6)

Answer 1

Hint: Here in this question, the area of parallelogram is to be found. to find the area of a parallelogram there is a standard formula and it is defined as \[A = base \times height\]. In the question the points of the parallelogram in a coordinate plane are mentioned. by using data, we construct the parallelogram and then find the area.

Complete step-by-step solution:
A parallelogram is a quadrilateral. In the parallelogram the two sides are parallel to each other and with equal measures. The parallelogram is a two-dimensional figure. therefore the area of parallelogram is given by \[A = base \times height\].

Here in this question the points on the coordinate plane are given as A (-4, -3) B (2, -3) C (4, -6) D (-2, -6). by using these points let we draw the parallelogram. By the diagram we can determine the value of base and the value of height.

If we consider the graph there are six boxes from point A to point B and it is the same as for point C and point D. Therefore the value of base of the parallelogram is 6 cm. The unit will cm since in the graph each box is 1cm. now there is a perpendicular line drawn from the point C to the line AB. that signifies the height of the parallelogram. therefore, the height of the parallelogram is 3 cm.
Hence, we know the value of base and height of parallelogram. Then the area of parallelogram is
 \[A = base \times height\]
Substituting the values to the formula we have
\[ \Rightarrow A = 6 \times 3\]
on simplifying we get
\[ \Rightarrow A = 18sq.cm\]

Therefore area of parallelogram is $18 sq.cm$

Note: A parallelogram is a closed two-dimensional figure. Generally the area is the region occupied by the two dimensional thing. The area of a parallelogram is defined as the region occupied by the parallelogram. It can be determined by using formula \[A = base \times height\]. The unit of area in general is \[sq.cm\]or \[sq.m\].