Pythagorean theorem + area of a shape - practice problems - page 8 of 23
Number of problems found: 449
- Equilateral triangle vs circle
Find the area of an equilateral triangle inscribed in a circle of radius r = 9 cm. What percentage of the circle area does it occupy? - Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long. - Right isosceles triangle
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into two equal segments. The length of one segment is 5 cm. What is the area of the triangle? - Diamond diagonals
Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square and the side length is 13 cm. - Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 810 cm. - Right-angled 82471
The lengths a = 7.2 cm and b = 10.4 cm are dropped in the right-angled triangle ABC. Do the math a) lengths of the sections of the hypotenuse b) height on the hypotenuse c - Diagonals 81884
In an isosceles trapezoid, the basic lengths are 15 cm and 9 cm. The diagonals are 13 cm long. Calculate the perimeter and area of the trapezoid. - Constructed 8161
The perimeter of the right triangle is 18 cm. The sum of the areas of the squares constructed above its three sides is 128cm². What is the area of the triangle? - Rectangular garden
The sides of the rectangular garden are in a ratio of 1:2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden. - Road embankment
Road embankment has a cross-section shape of an isosceles trapezoid with bases 5 m and 7 m and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Right-angled 81989
Using Euclid's Theorems and Pythagoras' Theorem, complete the following parameters describing a right-angled triangle ABC with a right angle at vertex C if we know b=10, cb=8 - Difference 80618
A regular hexagon is described and inscribed in a circle. The difference between its areas is 8√3. Find the circle's radius. - Calculate 47763
Calculate the area of an isosceles trapezoid ABCD, whose longer base measures 48 cm, the shorter base measures 3/4 of the longest base, and the leg of the trapezoid measures 2/3 of the longer base. The result is rounded to the nearest hundredth. - Isosceles 27793
The LICH isosceles trapezoid has 5.2 cm long arms and its bases are 7.6 cm and 3.6 cm long. Find the area of the LICH trapezoid. - Circumference 7823
The bases are 9 cm and 5 cm long in a rectangular trapezoid. The length of the shorter arm is 3 cm. Calculate its circumference and area. - Equilateral 4301
Triangle ABC is equilateral with a side length of 8 cm. Points D, E, and F are the sides AB, BC, and AC midpoints. Calculate the area of triangle DEF. In what ratio is the area of triangle ABC to the area of triangle DEF? - Flakes
A circle was inscribed in the square. We draw a semicircle above each side of the square as above the diameter. This resulted in four chips. Which is bigger: the area of the middle square or the area of the four chips? - Rectangular field
A rectangular field has a diagonal length of 169m. If the length and width are in the ratio of 12:5. Find the dimensions of the field, the perimeter of the field, and the area of the field. - Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Rhombus and diagonals
The rhombus area is 150 cm2, and the ratio of the diagonals is 3:4. Calculate the length of its height.
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