# Pythagorean theorem - examples - page 22

- Diagonal

he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal. - Area of iso-trap

Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other. - Embankment

Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long. - Solid cuboid

A solid cuboid has a volume of 40 cm^{3}. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Circle - AG

Find the coordinates of circle and its diameter if its equation is: ? - Equation of circle

find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16. - Equation of circle 2

Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x. - Rhombus

The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm. - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H - Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F. - Windbreak

A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree? - Surface area of the top

A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder. - A square

A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal. - Find the 5

Find the equation with center at (1,20) which touches the line 8x+5y-19=0 - Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Garden fence

The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced? - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Two people

Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar - Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m

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Pythagorean theorem is the base for the right triangle calculator.