Practice Example (heron) (9.4) - Properties of Triangles - IB 10 Mathematics

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6 sample questions

Question 1.
Use Heron's formula to find the area of a triangle with sides 5 cm, 12 cm and 13 cm.
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Find the semi-perimeter first.
Question 2.
A triangle has sides 6, 8 and 10. Find its semi-perimeter and its area.
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Subtract each side from s before multiplying.
3Question 3.
What is the semi-perimeter s of a triangle with sides a, b and c?
- (a + b + c)/2
- a + b + c
- (a + b + c)/3
- abc/2
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"Semi" means half.
4Question 4.
For the triangle with sides 7, 8 and 9, which product goes under the square root in Heron's formula?
- 12 × 5 × 4 × 3
- 24 × 17 × 16 × 15
- 7 × 8 × 9
- 12 × 7 × 8 × 9
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Use the semi-perimeter, not the full perimeter.
Question 5.
Quadrilateral ABCD has AB = 9, BC = 40, CD = 28 and DA = 15, and the diagonal AC = 41. Find the area of ABCD.
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Use Heron's formula on each triangle and add the areas.
Question 6.
Use Heron's formula to show that an equilateral triangle with side a has area (√3/4)a², and find the area when a = 6.
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All three brackets are equal in an equilateral triangle.

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