# Examples for 9th grade - page 50

- Quadrilateral

In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 96 cm^{2,}what is the area of ABCD? - Diamond

Rhombus has side 23 cm and and one of diagonal 36 cm long. Calculate its area. - Speedometer

The speedometer of a car reads 78 km/h. It's accurate to within 4.2% What is the maximum possible error? - Trapezoid ABCD v2

Trapezoid ABCD has length of bases in ratio 3:2. The area of riangle ACD is 956 dm^{2.}What is the area of trapezoid ABCD? - TV commercials

For the typical one-hour prime-time television slot, the number of minutes of commercials is 7/23 of the minutes of the actual program. Determine how many minutes of the program are shown in that one hour. - Round table

Round table with diameter d = 95 cm is coated by square tablecloth with a side length 122 cm. About how many cm is higher center of tablecloth than its cornes? - Axial section

Axial section of the cylinder has a diagonal 15 cm long and we know that the area of the side and the area of base is in ratio 1:1. Calculate the height and radius of the cylinder base. - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 40 m. Water depth at beginning of pool is 1.15 m (for children) and depth at end is 1.92 m (for swimmers). Slope express as percentage and as angle in degrees. - Two runners

Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute - Rectangles - sides

One side of the rectangle is 25 cm longer than second. Shortens longer side by 14 cm and extend shorter by 13 cm increases the area of the rectangle by 130 cm^{2.}What are the dimensions of the original rectangle? - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle. - SAS triangle

The triangle has two sides long 7 and 19 and included angle 144°11'59″. Calculate area of this triangle. - Rhomboid

Calculate the circumference and area of the rhomboid with sides 11 and 17, with their angle 70°. - Described

Calculate perimeter of the circle described by a triangle with sides 418, 59, 430. - Meridian

What is the distance (length) the Earth's meridian 27° when the radius of the Earth is 6370 km? - Sphere cuts

At what distance from the center intersects sphere with radius R = 60 plane, if the cut area and area of the main sphere circle is in ratio 3/6. - Glass of juice

Glass of juice shaped cylinder 16 cm height and base diameter of 10 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel. - Angles in triangle

The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle?

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