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

#### Number of problems found: 214

• Gardens The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
• Railway embankment The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• Area and perimeter of rectangle The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
• Extending square garden Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m2 (square), it had the shape of a square again. How many meters has the length of each side of the garden been extended?
• Sphere in cone A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
• Height The content of the triangle is 35 cm2. The length of the base is 10 cm. Determine the length of the height on the base.
• 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 cm2
• Edge of prism The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
• Cylinder container The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach? 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 surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
• 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 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. 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.
• Side lengths In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
• The right triangle The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
• 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.
• 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?
• 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.
• An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?

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