Diagonal - 9th grade (14y) - examples
- Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
- MO Z9–I–2 - 2017
In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
- 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.
Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long.
Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm?
- 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| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm.
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
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.
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.
- Axial section
Axial section of the cylinder has a diagonal 15 cm long and we know that the area of the side and the area of base is in ratio 1:1. Calculate the height and radius of the cylinder base.
- Square diagonal
Calculate the length of diagonal of the square with side a = 18 cm.
- Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
- Square 2
Points D[9,-1] and B[3,3] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 39 cm and the edge of the base is 24 cm. The edge length of the base of the prism and height is 3:2.