# Pythagorean theorem - examples - page 23

- Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Decagon

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

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area. - ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX? - Rectangular trapezoid

The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the. - Equilateral triangle

Calculate the area of an equilateral triangle with circumference 72cm. - Bamboo

Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm. - Quadrangular pyramid

Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area. - Ellipse

Ellipse is expressed by equation 9x^{2}+ 25y^{2}- 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse. - Is right triangle or not

If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area. - Body diagonal

Calculate the length of the body diagonal of the 6cm cube. - Is right-angled

Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle? - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - The pond

We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?

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Pythagorean theorem is the base for the right triangle calculator.