# Area of shape + expression of a variable from the formula - math problems

#### Number of problems found: 199

- Ratio of squares

A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares? - Cylinder container

The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach? - Wallpaper

3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide? - Square and circles

The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a. - Quadrilateral pyramid

A regular quadrilateral pyramid has a volume of 24 dm^{3}and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid - Quadrilateral pyramid

Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm. - In the

In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm^{2}. - Height to the base

The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base. - Quadrilateral prism

The surface of the regular quadrilateral prism is 8800 cm^{2}, the base edge is 20 cm long. Calculate the volume of the prism - Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - The funnel

The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel. - Dimensions of the trapezoid

One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm^{2} - Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm. - The circumference

The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length? - The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm^{2}. Calculate the length of the leg b and the median t2 to side b. - Cross five

The figure on the picture is composed of the same squares and has a content of 45cm². What's its perimeter? - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - Edge of prism

The regular quadrilateral prism has a surface of 250 dm^{2}, its shell has a content of 200 dm^{2}. Calculate its leading edge. - The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m.

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