Diagonal - 9th grade (14y) - examples
- 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?
- Tv screen
The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
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.
- Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm?
Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long.
- Rhombus ABCD
Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD.
Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm.
- Square diagonal
Calculate length of the square diagonal if the perimeter is 200 cm.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
- IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 39 cm, c = |CD| = 8 cm and legs b = d = |BC| = |AD| = 24 cm.
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
In rectangle ABCD with sides |AB|=11, |AD|=12 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
- Rhombus and inscribed
Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals.
- Axial section
Axial section of the cylinder has a diagonal 63 cm long and we know that the area of the side and the area of base is in ratio 1:3. Calculate the height and radius of the cylinder base.
- Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
- Square diagonal
Calculate the length of diagonal of the square with side a = 18 cm.
- Square 2
Points D[9,-1] and B[3,3] are opposed vertices of the square ABCD. Calculate area of the square ABCD.