Quadrilaterals and Polygons
Three vertices of a parallelogram $$ABCD$$ are $$A (3, -1, 2), B(1, 2, -4)$$ and $$C (-1, 1, 2)$$. Find the coordinates of the fourth vertex.
The perimeter of a parallelogram is 140 cm. If one of the sides is longer than the other by 10 cm,find the length of each of its sides.
Given that one of the sides is longer than the other by $$10\ cm$$ and let it be $$x$$ and $$x+10$$
Also given that its perimeter is $$140\ cm$$
But we know that perimeter $$=2(length + width)=2(x+(x+10))$$
$$140=2(2x+10)$$
$$140=4x+20$$
$$140 -20=4x$$
$$x=120/4=30$$
$$x=30\ cm$$
$$x+10=40\ cm$$
Therefore the side are $$30\ cm$$ and $$40\ cm$$.
Three vertices of a parallelogram $$ABCD$$ are $$A (3, -1, 2), B(1, 2, -4)$$ and $$C (-1, 1, 2)$$. Find the coordinates of the fourth vertex.
The measures of two adjacent angles of a parallelogram are in the ratio $$3 : 2$$. Find the measure of each of the angles of the parallelogram.
The sum of two opposite angles of a parallelogram is $$130^o$$. Find the measure of each of its angles.
The measure of two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each angle of the parallelogram.
$$ABCD$$ is a parallelogram in which $$\angle {110^{o}}.$$ Find the measure of each of angles $$\angle B,\ \angle C$$ and $$\angle D.$$
Two adjacent angles of a parallelogram are $$\left(2x+25\right)^{o}$$ and $$\left(3x-5\right)^{o}.$$ The value of $$x$$ is
The diagonals do not necessarily intersect at right angles in a
Two adjacent side of a parallelogram are 15 cm. If the distance between the longer sides is 8 cm , find the ares of the parallelogram. Also find the distance between shorter sides.
Show that the diagonals of a parallelogram divide it into four triangles of equal area.
(a) In the figure ( 1 ) given below, the perimeter of parallelogram is $$ 42 \mathrm{cm} $$. Calculate the lengths of the sides of the parallelogram.