a The heights are the dashed vertical segments that run between the parallel sides of each trapezoid.
B
b Use the similarity between the figures to find the length of the parallel sides in the larger trapezoid.
A
a 3 or 13
B
b 9 or 19
Practice makes perfect
a The heights of the given trapezoids are represented by the vertical dashed segments between the trapezoid'sparallel sides. Examining the diagram, we see that these are 11 cm and 33 cm. Depending on how we compare the trapezoids, there are two possible ratios.
MAET/EKIM& = 33/11= 3 or [2em]
EKIM/MAET& = 11/33=1/3
The ratio is either 3 or 13 depending on how we choose to compare the figures. The larger trapezoid's height is 3 times greater then the height of the smaller trapezoid, but you can also say that the smaller trapezoid's height is a third of the larger trapezoid's.
b The area of a trapezoid is the sum of its parallel sides, multiplied by its height, and divided by 2.
A=1/2h(b_1+b_2)
The smaller trapezoid has all the necessary information to calculate the area. However, this is not the case for the larger trapezoid. Let's label the two parallel sides and highlight the corresponding sides in MAET.
In similar shapes, the ratio between any pair of corresponding sides is always the same. With this information, we can write two equations.
b_1/MA=3 and b_2/TE=3
By substituting the lengths of MA and TE in these equations, we can determine b_1 and b_2.
Now we have all of the information needed to calculate the area of both parallelograms.
A_(MAET)&=1/2(11)(20+30) = 275 cm^2 [1.5em]
A_(EKIM)&= 1/2(33)(60+90) = 2475 cm^2
Finally, we can calculate the ratio between the trapezoid's area. As in Part A, there are two possibilities depending on which ratio you calculate.
&A_(EKIM)/A_(MAET)=2475/275=9 or [1.5em]
&A_(MAET)/A_(EKIM)=275/2475=1/9
