Practice problems of the triangle - page 65 of 117
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the measures of the interior angles of a triangle is always 180 degrees. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The best known area formula is T = a*h /2 where a is the length of the side of the triangle, and h is the height or altitude of the triangle.Number of problems found: 2330
- Circumscribed 83152
Given is an isosceles triangle whose base is 8 cm, and the sides are 15 cm long. Calculate the area of the triangle and the radius of the inscribed and circumscribed circle. - Isosceles 7566
A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How much percent does the triangle occupy the area of the circle? - Triangle 3552
Draw a circle k (S, r = 3cm). Build a triangle ABC so that its vertices lie on the circle k and the length of the sides is (AB) = 2.5 cm (AC) = 4 cm - Two heights and a side
Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm, and height to side b: vb = 4 cm.
- Diagonals 5113
In the diamond KLMN, the lengths of the diagonals are 10 cm and 6 cm. Determine the angle size that the longer diagonal makes with the side of the diamond. - The rectangular
The rectangular trapezoid has bases 15 dm and 8 dm long, and the length of the inclined arm is 12 dm. How long is the other arm of the trapezoid? - Diagonal in rectangle
In the ABCD rectangle is the center of BC, point E, and point F is the center of the CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Kites
Boys run kites on a cable of 68 meters long. What is the kite altitude if the angle from the horizontal plane is 72°? - Trapezoid 2520
Trapezoid with sides a = 10, b = 20, c = 25, d = 15. Calculate all internal angles.
- Circle described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Circumferential angle
Vertices of the triangle ΔABC lay on the circle and are divided into arcs in the ratio 7:8:7. Determine the size of the angles of the triangle ΔABC. - Diamond and angles
The internal angles in the diamond are 60° and 120°. Its side is 5 cm long. Find the area of a diamond. - Rhombus
One angle of a rhombus is 136°, and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - The rope
A 68-centimeter-long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimeters. What is the distance between the other two corners?
- Raindrops
The train is moving at a speed of 60 km/h. Raindrops falling vertically in the absence of wind (with uniform movement due to the action of air resistance) leave traces on the windows of the train, deviating from the vertical direction by 30°. How fast are - Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm. - Trapezoid ABCD
Calculate the perimeter of trapezoid ABCD if we know the side c=12, b=19, which is also a height, and side d=32. - Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof; if 5.5% of the sheet, we must add for joints and waste. - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm².
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