Question

What is the area of parallelogram rstu? 21 square units 24 square units 28 square units 32 square units

Answer 1

The area of the considered parallelogram RTSU is given by: Option A: 21 sq. units

How to find the area of a parallelogram?

Area of a parallelogram  = (its height × its base) sq. units.

What is the distance between two points ( p,q) and (x,y)?

The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

$D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units$

For this case, the missing diagram is attached below.

If we take the base as ST then as ST is parallel to y axis, the line perpendicular to ST would be parallel to x axis. The heigth of a parallogram  is the perpendicular distance between its base and top.

The base is ST and top is RU, the line segment US is perpendicular to both RU and US and its length,therefore, will serve as height as its length=perpendicular distance between the base and the top of the parallelogram.

Thus, we get:

Area of RTSU = Length of ST × Length of US

The coordinates of endpoints of ST are (4,-1), (4,-4)

Thus, the length of ST = distance between S and T = $\sqrt{(4-4)^2 + (-1 - (-4))^2 }= 3$

The coordinates of endpoints of US are (-3,-1), (4,-1)

Thus, the length of US = distance between U and S = $\sqrt{(-3-4)^2 + (-1 - (-1))^2 }= 7$

Thus, Area of RTSU = Length of ST × Length of US = 3 × 7 = 21 sq. units.

Thus, the area of the considered parallelogram RTSU is given by: Option A: 21 sq. units

Learn more about distance between two points here:

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