What is Heron's formula for the area of a triangle?

Heron's formula states that the area $$A = \text{sqrt}(s(s-a)(s-b)(s-c))$$ , where $$s = \frac{a + b + c}{2}$$ .

What is the area of a triangle with sides of lengths 5 m, 6 m, and 7 m?

Using Heron's formula, first find the semi-perimeter $$s = \frac{5 + 6 + 7}{2} = 9$$ . Then, the area is $$A = \text{sqrt}(9(9-5)(9-6)(9-7)) = \text{sqrt}(9 \times 4 \times 3 \times 2) = 12 \text{ m}^2$$ .

What is the unit of area for a triangle measured in meters?

The unit of area is square meters (m²).

If the area of a triangle is 30 m² and the base is 10 m, what is the height?

Using the area formula, $$30 = \frac{1}{2} \times 10 \times height$$ , so height = 6 m.

What is the area of a triangle with a base of 15 yd and a height of 8 yd?

The area is $$A = \frac{1}{2} \times 15 \times 8 = 60 \text{ yd}^2$$ .

If a triangle has an area of 40 square inches and a base of 8 inches, what is the height?

Using the area formula, $$40 = \frac{1}{2} \times 8 \times height$$ , so height = 10 inches.

What is the relationship between the base and height of a triangle in calculating its area?

The area of a triangle is directly proportional to both the base and the height; if either increases, the area increases.

Area of a triangle Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the formula to calculate the area of a triangle?

Back

2.

FLASHCARD QUESTION

Front

What does 'base' refer to in the context of a triangle?

Back

The 'base' of a triangle is any one of its sides, typically the one on which the triangle is considered to be standing.

3.

FLASHCARD QUESTION

Front

What does 'height' refer to in the context of a triangle?

Back

The 'height' of a triangle is the perpendicular distance from the base to the opposite vertex.

4.

FLASHCARD QUESTION

Front

If a triangle has a base of 10 cm and a height of 5 cm, what is its area?

Back

5.

FLASHCARD QUESTION

Front

What is the area of a triangle with a base of 8 m and a height of 4 m?

Back

6.

FLASHCARD QUESTION

Front

What is the area of a triangle with a base of 12 inches and a height of 3 inches?

Back

7.

FLASHCARD QUESTION

Front

How do you find the area of a triangle if you only know the lengths of all three sides?

Back

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