Area + Pythagorean theorem - practice problems
Number of problems found: 645
- The rhombus (a,d)
Find the area of a rhombus, one side of which measures 20 cm, and one diagonal 24 cm. - A field
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m and the non parallel sides are 14 m and 13 m. Find the area of the field. - Isosceles triangle 17
One of the equal sides of an isosceles triangle is 13 cm and its perimeter is 50 cm. Find the area of the triangle. - Grassland and goat
An unfenced grassland is a right triangle ABC with AB = 4m, BC = 8m, and AC as hypotenuse. A goat is tied to a 5-m long rope with its stake at point O, which is 2m from side AB and 2m from the prolongation of side BC through corner B. Then: 1. How far is
- Incircle to circumcircle
Find the ratio of the areas of the incircle and the circumcircle of a square. - PQR - Euclid
Find the length of line segment PR - leg of the right triangle PQR. PQ=17 cm PS=15 cm QS=8 cm; Point S is the height touch point with a hypotenuse of the RQ. - Find area 2
Find the area of the green region in the given picture. Dimensions are shown. - Smaller square
Let the points A, B, C and D are midpoints of the sides of the square PQRS. If the area of PQRS is 100 sq cm, what is the area of the smaller square ABCD? - Parallelogram - right angles
In parallelogram ABCD; AB = 16 cm, BC = 12 cm and diagonal AC = 20 cm. Find the area of the parallelogram.
- Circle inscribed square
What is the area of the circle that can be inscribed in a square of 10 cm? - ET inscribed circle
An equilateral triangle has been inscribed in a circle with a radius of 4 cm . Find the area of the shaded region. - Cuboid - sum of edges length
Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - A frustum
A frustum of a pyramid consists of a square base of length 10 cm and a top square of length 7 cm. The height of the frustum is 6 cm. Calculate the surface area and volume. - A lamp
A lamp shade like that of a frustum has a height of 12 cm and an upper and lower diameter of 10 cm and 20 cm. What area of materials is required to cover the curved surface of the frustum?
- Circumference 83645
The area of a right triangle is 240 cm². Determine its circumference if the given lengths are suspended in a ratio of 5:12. - Connecting 83441 They are given a square ABCD. The points EFGH are the midpoints of its sides. What part of the content of the square ABCD is the content of the square created in its center by connecting the points AF, BG, CH, and DE?
- Circumscribed 83363
Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle. - Quadrilateral pyramid
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid. - Equilateral 83322 The glass weight has the shape of a regular four-sided pyramid with a base edge of 10 cm. The shell walls are equilateral triangles. What is the weight in grams of the paperweight if the density of the glass is 2500kg/m³?
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