2000005502
Level:
A
Which side of the quadrilateral shown in the picture is the longest?
\(a\)
\(b\)
\(c\)
\(d\)
Polygons
2000005503
Level:
A
The diagonals of a quadrilateral \(ABCD\) are halved and perpendicular to each other. What type of quadrilateral is it?
square or rhombus
rhombus
square
rectangle or square
2000005504
Level:
A
Let \(ABCD\) be an arbitrary convex quadrilateral and let’s denote by \(P\), \(Q\), \(R\), \(S\) the centers of the sides \(AB\), \(BC\), \(CD\), \(DA\) in that order. Then, what type of a quadrilateral is \(PQRS\)?
It may or may not be a parallelogram.
It is a rectangle.
It is a rectangle or a square.
It is not a parallelogram.
2000005505
Level:
A
What is the perimeter of the rhombus \(ABCD\), if \(|BD|=8\,\mathrm{cm}\) and \(|\measuredangle DAB|=60^{\circ}\) (see the picture)?
\(32\,\mathrm{cm}\)
\(16\,\mathrm{cm}\)
\(28\,\mathrm{cm}\)
\(36\,\mathrm{cm}\)
2000005506
Level:
A
The picture shows a triangle \(ABC\) with a central transversal \(EF\). The area of the trapezoid \(ABFE\) is \(24\,\mathrm{cm}^2\). What is the area of the triangle \(EFC\)?
\(8\,\mathrm{cm}^2\)
\(4\,\mathrm{cm}^2\)
\(16\,\mathrm{cm}^2\)
\(12\,\mathrm{cm}^2\)
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?
\(10\,\mathrm{cm}^2\)
\(20\,\mathrm{cm}^2\)
\(5\,\mathrm{cm}^2\)
\(8\,\mathrm{cm}^2\)
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?
\(\frac{5}{3}\,\mathrm{cm}\)
\(\frac{4}{3}\,\mathrm{cm}\)
\(\frac{10}{3}\,\mathrm{cm}\)
\(2\,\mathrm{cm}\)
2000005509
Level:
A
Calculate the area of a rhombus whose perimeter is \(2\,\mathrm{m}\) and lengths of its diagonals are in the ratio \(3:4\).
\(2\,400\,\mathrm{cm}^2\)
\(1\,800\,\mathrm{cm}^2\)
\(3\,600\,\mathrm{cm}^2\)
\(2\,000\,\mathrm{cm}^2\)
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
2010006705
Level:
A
The perimeter of a rectangle is \(22\, \mathrm{cm}\).
The diagonal of this rectangle is \(\sqrt{65}\, \mathrm{cm}\).
Find the sides of the rectangle.
\(7\, \mathrm{cm}\)
and \(4\, \mathrm{cm}\)
\(14\, \mathrm{cm}\)
and \(8\, \mathrm{cm}\)
\(6\, \mathrm{cm}\)
and \(5\, \mathrm{cm}\)
\(10\, \mathrm{cm}\)
and \(1\, \mathrm{cm}\)