Triangles Test ...

In Figure , $$AB = BC$$. If the area of $$\triangle$$ $$ABE$$ is $$x$$, calculate the area of $$\triangle$$ $$ACD$$.

In the figure below, $$\angle ABC=\angle DFE,\angle BAC=\angle FDE$$, $$D$$ and $$F$$ are on $${ AB } ,\ { AD } ={ FB } $$ and the distances are shown in the figure itself in centimeters. Calculate the length of $${ AD } $$, in centimeters.

In the following figure, what is the value of $$x$$ in terms of $$y$$?

In the given figure, find the value of $$AE$$ if $$AC = 5.6$$ cm and $$DE || BC$$.

In similar triangles $$\triangle ABC$$ and $$\triangle FDE, DE = 4 cm, BC = 8 cm$$ and area of $$\triangle FDE = 25 cm^2$$. What is the area of $$\Delta ABC$$?

What is the ratio of the areas of two similar triangles whose corresponding sides are in the ratio 15:19?

In the figure shown above, $$DE$$ is parallel to $$BC$$ and the ratio of the areas of $$\triangle ADE$$ and trapezium $$BDEC$$ is $$4 : 5$$. What is $$DE : BC$$?

The areas of two similar triangles are 100 $$\mathrm{cm^2}$$ and 64 $$\mathrm{cm^2}$$ respectively. If the median of greater side of the first triangle is 13 cm, find the corresponding median of the other triangle.

In Figure , $$\overline{QR} = \overline{RS}$$. If the area of $$\triangle RST$$ is $$\dfrac{c}{2}$$, what is the area of $$\triangle QSP$$?

In Figure , $$\overline{EG} || \overline{DH}$$, and the lengths of segments $$\overline{DE}$$ and $$\overline{EF}$$ are as marked. If the area of $$\triangle EFG$$ is a, calculate the area of $$\triangle DFH$$ in terms of $$a$$.