Q: Given the formula for the area of a triangle: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$, what is the area of a triangle with a base of 6 units and a height of 4 units?

$$A = \frac{1}{2} \times 6 \times 4 = 12$$

Q: In the context of the graphs shown, if the red and blue lines intersect at (2, 4), what is the area of the triangle formed by the x-axis, the y-axis, and the line segment from (0,0) to (2,4)?

$$A = \frac{1}{2} \times 2 \times 4 = 4$$

Q: Suppose you have a triangle with vertices at (0,0), (4,0), and (4,3). What is the area of this triangle?

$$A = \frac{1}{2} \times 4 \times 3 = 6$$

Q: If the area of a triangle is 10 square units and the base is 5 units, what is the height?

$$h = \frac{2A}{b} = \frac{2 \times 10}{5} = 4$$

Q: A triangle has an area of 8 square units and a height of 4 units. What is the length of the base?

$$b = \frac{2A}{h} = \frac{2 \times 8}{4} = 4$$

Question 1

Given the formula for the area of a triangle: $$A = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$$, what is the area of a triangle with a base of 6 units and a height of 4 units?

Accepted Answer

$$A = \frac{1}{2} 	imes 6 	imes 4 = 12$$

Question 2

In the context of the graphs shown, if the red and blue lines intersect at (2, 4), what is the area of the triangle formed by the x-axis, the y-axis, and the line segment from (0,0) to (2,4)?

Accepted Answer

$$A = \frac{1}{2} 	imes 2 	imes 4 = 4$$

Question 3

If the base of a triangle is doubled while the height remains the same, how does the area change?

Accepted Answer

The area doubles.

Question 4

Suppose you have a triangle with vertices at (0,0), (4,0), and (4,3). What is the area of this triangle?

Accepted Answer

$$A = \frac{1}{2} 	imes 4 	imes 3 = 6$$

Question 5

If the area of a triangle is 10 square units and the base is 5 units, what is the height?

Accepted Answer

$$h = \frac{2A}{b} = \frac{2 	imes 10}{5} = 4$$

Question 6

A triangle has an area of 8 square units and a height of 4 units. What is the length of the base?

Accepted Answer

$$b = \frac{2A}{h} = \frac{2 	imes 8}{4} = 4$$

Question 7

If the area of a triangle is calculated as $$A = \frac{1}{2} 	imes 6 	imes 2$$, what is the area?

Accepted Answer

$$A = 6$$

Question 8

Which of the following statements is true about the area of a triangle?

Accepted Answer

The area is always half the product of its base and height.

Question 9

If a triangle's base is increased by 50% and its height is decreased by 50%, what happens to the area?

Accepted Answer

The area remains the same.

Question 10

Given a triangle with base $$b$$ and height $$h$$, which of the following correctly rearranges the area formula to solve for $$h$$?

Accepted Answer

$$h = \frac{2A}{b}$$

Using the Area of a Triangle in Microeconomics: Applications to Graphs

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