# Examples for 8th grade - page 52

- Leg

Determine the area of a trapezoid with bases 60 and 37 and height is 3 shorter than the its leg. - Sales vs profit

Apple sells 45 percent less computes than the Acer but the profit from their sales is 1.7 times higher than Acer. How many times are Apple computer more expensive than Acer? - Sector

The perimeter of a circular sector with an angle 2 rad is 53 cm. Determine the radius of the circle from which the sector comes. - Cyclists

Cyclist who rides at an average speed 17 km/h travels trip distance 14 min before the cyclist who rides at an average speed 15 km/h. What is the length of this cyclist trip(distance in km)? - Car

Car goes from point A to point B at speed 70 km/h and back 76 km/h. If they goes there and back at speed 73 km/h trip would take 19 minutes shorter. What is distance between points A and B? - Road embankment

Road embankment has a cross section shape of an isosceles trapezoid with bases 9 m and 12 m, and 4 m long leg. How many cubic meters of soil is in embankment length of 758 meters? - Road

Average climb of the road is given by ratio 1:29. By what angle road average climb? - Divisibility

Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2. - Climb

On the road sign, which informs the climb is 20%. Car goes 5 km along this road. What is the height difference that car went? - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 4772 cm^{3.}Calculate the radius of the base circle and height of the cone. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-9,-8] and B[-8,0]? - Parallelogram

Calculate area of the parallelogram ABCD as shown if |AB| = 45 cm, |BC| = 23 cm and angle BAD = 30° - Rhombus

Internal angles of rhombus is in ratio 3:6. How many times is the shorter diagonal longer than side of rhombus? - Area 4gon

Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 7, 15, 7 and 15. Inner angles are 45°, 135°,45°, 135°. - Triangle

Calculate the area of right triangle ΔABC, if one leg is long 12 and its opposite angle is 31°. - Equator

Suppose that tourist went on foot over the Globe equator. How many meters more track made his hat on his head as the shoes on your feet? The radius of the earth is 6378 km and height of the tourist is 1.7 m. - Election mathematics

In elections, 6 political parties received this shares of voters: strana A 69.4 %strana B 11.2 %strana C 10.2 %strana D 7.6 %strana E 1.6 % Calculate what the shares acquired in the parliament, if a quorum is 5%. - Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Job task

After two hours and 40 minutes the job is finished. Compared to last year we were 40 minutes faster. What is the percentage increase to our performance? - Parallelogram

Side a of parallelogram is twice longer than side b. Its circumference is 78 dm. Calculate the length of the sides of a parallelogram.

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