Assume the following values for the diagrams below: Q1 = 15 bags. Q2 = 10 bags. Q3 = 22 bags. The market equilibrium price is $25 per bag. The price at point a is $70 per bag. The price at point c is $10 per bag. The price at point d is $40 per bag. The price at point e is $20 per bag. The price at point f is $32 per bag. The price at point g is $4 per bag. Apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the following questions.

Question

Assume the following values for the diagrams below: Q1 = 15 bags. Q2 = 10 bags. Q3 = 22 bags. The market equilibrium price is $25 per bag. The price at point a is $70 per bag. The price at point c is $10 per bag. The price at point d is $40 per bag. The price at point e is $20 per bag. The price at point f is $32 per bag. The price at point g is $4 per bag. Apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the following questions.

Answer 1

To apply the formula for the area of a triangle (Area = ½ × Base × Height) to answer the questions related to the diagrams, we need to identify the base and height of each triangle. The base of a triangle is the difference in quantity (Q) between two points, and the height is the difference in price (P) between the same two points.

Let's go through each question and identify the base and height for each triangle:

1. What is the area of the triangle formed by points a, g, and e?

- The base is the difference in quantity between points a and g: Qa - Qg = 15 - 0 = 15 bags.
- The height is the difference in price between points a and g: Pa - Pg = $70 - $4 = $66 per bag.
- Applying the area formula: Area = ½ × Base × Height = ½ × 15 × $66 = $495.

2. What is the area of the triangle formed by points f, g, and e?

- The base is the difference in quantity between points f and g: Qf - Qg = 10 - 0 = 10 bags.
- The height is the difference in price between points f and g: Pf - Pg = $32 - $4 = $28 per bag.
- Applying the area formula: Area = ½ × Base × Height = ½ × 10 × $28 = $140.

3. What is the area of the triangle formed by points c, d, and g?

- The base is the difference in quantity between points c and g: Qc - Qg = 22 - 0 = 22 bags.
- The height is the difference in price between points c and g: Pc - Pg = $10 - $4 = $6 per bag.
- Applying the area formula: Area = ½ × Base × Height = ½ × 22 × $6 = $66.

Please note that these calculations assume the triangles formed by the points are right-angled triangles and that the points on the diagram represent the vertices of the triangles.