The lengths of two parallel sides of a trapezium are 10 cm and 15 cm. The lengths of other two sides are 4 cm and 6 cm. How will you find out the area and magnitudes of 4 angles of the trapezium?

Question

The  lengths of two parallel sides of a trapezium are 10 cm and 15 cm. The lengths of other two sides are 4 cm  and 6 cm. How will you find out the area and magnitudes of  4 angles of the trapezium?

Avery Allen · Accepted Answer

so, from the figure, we know:

#h^2 +x^2 = 16# ................(1)

#h^2+y^2 = 36# ................(2)

and, #x+y = 5# ................(3)

#(1)-(2) => (x+y)(x-y)= -20\ #

#=>y-x = 4# (using eq. (3))..... (4)

so, #y = 9/2 # and #x = 1/2#

and so, #h = sqrt63/2#

From these parameters the area and the angles of the trapezium can be obtained easily.

Sadie Adams · Answer

undefined To find the area and magnitudes of the four angles of the trapezium:

1. First, calculate the height of the trapezium using the formula for the height of a trapezium:
   $$ \text{Height} = \sqrt{\text{Side Length}^2 - (\text{Top Base} - \text{Bottom Base})^2} $$

2. Then, calculate the area of the trapezium using the formula:
   $$ \text{Area} = \frac{1}{2} (\text{Sum of the lengths of the parallel sides}) \times (\text{Height}) $$

3. To find the magnitudes of the angles, you can use trigonometric functions or the properties of a trapezium:
   - The two angles at the shorter base are equal because the sides are parallel.
   - The sum of the measures of the angles at the longer base is 180 degrees.

4. Once you know the measures of the angles at the bases, you can find the measures of the other two angles using the fact that the sum of the angles of a quadrilateral is 360 degrees.