In the kite \( ABCD \), \( |AB| = |BC| = 12\,\mathrm{cm} \), \( |CD| = |DA| = 6\,\mathrm{cm} \), and the measure of \( \measuredangle DAB \) is \( 120^{\circ} \). Calculate the area of the kite.
A rectangle-shaped land has dimensions \(5 \times 8\,\mathrm{cm}\) on a map with scale \(1:500\). The owner increased the size of his land by buying some land from his neighbor. The new land has dimensions \(7\times 9\,\mathrm{cm}\) on the map. Find the actual increase of the perimeter of the land (i.e. find the increase in the length of the fence required to enclose the whole land). Give your answer in meters.
A rectangle-shaped land has dimensions
\(3\times 5\, \mathrm{cm}\) on a map with
scale \(1\colon 2\: 000\). The
owner increased the size of his land by buying some land from his neighbor. The new land has
dimensions \(4\times 5\, \mathrm{cm}\)
on the map. Find the actual increase of the perimeter of the land (i.e. find the
increase in the length of the fence required to enclose the whole land). Give your
answer in meters.
Two hotels and a lake are in a satellite photo. The distance between the hotels is
\(400\, \mathrm{m}\) which
is \(4\, \mathrm{cm}\)
in the photo. The area of the lake in the photo is
\(30\, \mathrm{cm}^{2}\). Find
the real area of the lake.
\(3\cdot 10^{5}\, \mathrm{m}^{2}\)
\(3\cdot 10^{1}\, \mathrm{m}^{2}\)
\(3\cdot 10^{3}\, \mathrm{m}^{2}\)
There is not enough information to solve this problem.