Calculating the area of any triangle when the height is not known

12 questions

1. Match the areas of these triangles with their dimensions.
2. Which of the following calculate the area of this triangle?
3. The area of this triangle, given to 2 significant figures, is ___cm^2.
4. A right angled triangle has a height of 12 cm and a hypotenuse of 13 cm. Work out the area.
5. Six equilateral triangles are put together to make a regular hexagon. The length of each triangle is 3 cm. Work out the exact area of the regular hexagon.
6. An isosceles triangle has a base of 4 cm and base angles of 68.2°. Select the correct area given to 2 significant figures.
7. A right-angled triangle has a height of 12 cm and a hypotenuse of 15 cm. The area of the triangle is ___cm^2.
8. An isosceles triangle has lengths 26 cm, 26 cm and 20 cm. The area of the isosceles triangle. is ___cm^2.
9. A triangle is drawn. The adjacent lengths are 7 cm and 9 cm with a 47° angle in between. The area of the triangle, to 1 decimal place, is ___cm^2.
10. An equilateral triangle has lengths of 6 cm. The area of the triangle, to 1 decimal place, is ___cm^2.
11. Two adjacent lengths of a triangle are x cm and 6 cm with a 47° angle in between. The area is 26.3 cm^2. Work out the value of x , giving your answer rounded to the nearest integer.
12. An equilateral triangle with lengths of x cm is drawn. It has an area of 3.9 cm^2. Work out the length of the equilateral triangle, giving your answer as a whole number.

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