Polygons

2000006004

Level: 
B
In the parallelogram \(ABCD\), the side \(AB\) is \(10\,\mathrm{cm}\) long, the diagonal \(AC\) measures \(15\,\mathrm{cm}\). The distance of the vertex \(D\) from the diagonal \(AC\) is \(2\,\mathrm{cm}\). What is the distance of the vertex \(D\) from the side \(AB\)?
\(3\,\mathrm{cm}\)
\(4\,\mathrm{cm}\)
\(5\,\mathrm{cm}\)
\(6\,\mathrm{cm}\)

2000005510

Level: 
A
The lengths of the sides of the rectangular garden are in the ratio \(3:4\). The line connecting the centers of adjacent sides is \(25\,\mathrm{m}\) long (see the picture). How long will it take for the owner to till the whole garden if he digs over \(1\,200\,\mathrm{dm}^2\) per hour?
\(100\) hours
\(50\) hours
\(30\) hours
\(40\) hours

2000005508

Level: 
A
A rectangle with sides \(3\,\mathrm{cm}\) and \(4\,\mathrm{cm}\) long is divided by one of its diagonals into two triangles. What is the distance of the centers of gravity of these two triangles?
\(\frac{5}{3}\,\mathrm{cm}\)
\(\frac{4}{3}\,\mathrm{cm}\)
\(\frac{10}{3}\,\mathrm{cm}\)
\(2\,\mathrm{cm}\)

2000005507

Level: 
A
We cut two triangles from the rectangular plate so that the resulting trapezoid has an area of \(30\,\mathrm{cm}^2\). One of its bases is twice as long as the other. What is the area of the two triangles that are cut off?
\(10\,\mathrm{cm}^2\)
\(20\,\mathrm{cm}^2\)
\(5\,\mathrm{cm}^2\)
\(8\,\mathrm{cm}^2\)