# Examples for secondary school students

- Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. - Adam and Ben

When Ben is so many years old to Adam today, Adam will be 23 years old. When Adam was as old as Ben, Ben was two years old. How old is today Ben and Adam? - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow - Inner angles

The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places. - Regular n-gon

In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon. - Photocopier

A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page? - Sequence 11

What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ? - Arithmetic progression

In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ? - Cuboid edges in ratio

Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm^{3.} - Tricolors

From the colors - red, blue, green, black and white, create all possible tricolors. - Krkonose CZ

Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3,}a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Average speed 4

Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip? - Roof 7

The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate? - Hollow sphere

The volume of the hollow ball is 3432 cm^{3.}What is its internal radius when the wall thickness is 3 cm? - BTC bubble

One of the world's experts in bubbles -- Prof. Robert Shiller, a Yale economist -- said Bitcoin "was an amazing example of a bubble" back in 2014. If you exchange fiat US dollar $100 to BTC in 2010, now in 2017 have value of 72.9 millions dollars. Find. - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?

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