Square root + Pythagorean theorem - math problems

Number of problems found: 138

How to
How to find a total surface of a rectangular pyramid if each face is to be 8 dm high and the base is 10 dm by 6 dm.
Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
Calculate
Calculate the height to the base of the isosceles triangle ABC if the length of the base is c = 24cm and the arms have a length b = 13cm.
ABC isosceles
ABC isosceles rights triangle the length or each leg is 1 unit what is the length of the hypotenuse AB in the exact form
Regular 4-sided pyramid
Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m.
The storm
The top of the 5 m high mast deviated by 1 m from the original vertical axis after the storm. What is the peak now? Round to 2 decimal places.
Calculate
Calculate the height of an isosceles triangle with base 37.8 mm long and an arm 23.1 mm long.
Total area
Calculate the total area (surface and bases) of a prism whose base is a rhombus which diagonals of 12cm and 18cm and prism height is 10 cm.
Rhombus and diagonals
The lengths of the diamond diagonals are e = 48cm, f = 20cm. Calculate the length of its sides.
Ladder
How long is a ladder that touches on a wall 4 meters high, and its lower part is 3 meters away from the wall?
Five circles
On the line segment CD = 6 there are 5 circles with a radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE.
Calculate 7
Calculate the height of the trapezoid ABCD, where coordinates of vertices are: A[2, 1], B[8, 5], C[5, 5] and D[2, 3]
Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?
Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.
Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
A kite
Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?
Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?