Question

Trapez równoramienny ABCD, którego pole jest równe 72 cm2, podzielono na trójkąt AED i trapez EBCD. Odcinek AE ma długość równą 4 cm, a odcinek CD jest od niego 2 razy dłuższy. Oblicz pole trójkąta AED. Zapisz obliczenia.

Answer 1

Answer:

The area of triangle AED is 12 square centimeters

Step-by-step explanation:

The question in English is

The isosceles trapezoid ABCD, whose area is equal to 72 cm2, is divided into an AED triangle and a EBCD trapezoid. The AE segment is 4 cm long and the CD segment is 2 times longer. Calculate the area of the AED triangle. Save the calculations.

The picture of the question in the attached figure

step 1

Find the length side DE

we know that

The area of the trapezoid ABCD is given by the formula

$A=\frac{1}{2} (CD+AB)DE$

$A=72\ cm^2$

so

$72=\frac{1}{2} (CD+AB)DE$

we have

$AE=4\ cm\\CD=2(4)=8\ cm\\AB=2AE+CD=2(4)+8=16\ cm$

substitute

$72=\frac{1}{2} (8+16)DE$

solve for DE

$144=24DE\\DE=144/24\\DE=6\ cm$

step 2

Find the area of triangle AED

The area of triangle AED is given by the formula

$A=\frac{1}{2}(AE)(DE)$

substitute the given values

$A=\frac{1}{2}(4)(6)=12\ cm^2$