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## Theme: “The area of shapes. Pythagoras’ Theorem.” 1 variant.

- Find the area of a parallelogram if one of its sides is 6 cm and the height to this side is 9 cm.
- The cathetus of an isosceles right triangle is 8 cm. Find the area of the triangle.
- In an isosceles trapezoid, the smaller base is 4 cm, the height is 3 cm, and the angle at the larger base is 45o. Find the area of the trapezoid.
- Find the side of a square if its diagonal is 5 cm.
- Find the side of an isosceles triangle if its base is 24 cm and the height given to the base is 9 cm.
- Find whether the triangle is right-angled if its sides are expressed by numbers 9, 12, 15. Justify the answer.

## Theme: “The area of shapes. Pythagoras’ Theorem.” Option 2.

- Find the area of a trapezoid if the smaller base is 7 cm, the larger base is 11 cm, and the height, 4 cm.
- The cathetus of an isosceles right triangle is 6 cm. Find the area of the triangle.
- The acute angle of a parallelogram is 30o, and the altitudes from the apex of the obtuse angle are 2cm and 3cm. Find the area of the parallelogram.
- The sides of a rectangle are equal to 12cm and 5cm. What is its diagonal equal to?
- The diagonals of a rhombus are equal to 8cm and 6cm. What is equal to its side?
- Find out if a triangle is right-angled if its sides are expressed by the numbers 15, 20, 25. Justify the answer.

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