Question

Which has the greater area, a triangle with a base of 50 feet and a height of 50 feet, or a circle with a diameter of 50 feet? Justify your answer.

Answer 1

Apply formula, Calculate and solve

Explanation:

formula for triangle = ½bh²

area of circle = πr² here r = radius = diameter/2

Hope it helped

Answer 2

The circle has a greater area than the triangle.

Explanation:

Area of a triangle:

• Aₜ = 1/2bh

Area of a circle:

• A꜀ = πr²

We are given the base and the height of the triangle, 50 ft and 50 ft respectively.

Substitute these values into the formula for the area of a triangle.

• Aₜ = 1/2(50)(50)
• Aₜ = 1/2(2500)
• Aₜ = 1250 ft²

The area of the triangle with a base of 50 ft and a height of 50 ft is 1250 ft².

We are given the diameter of the circle, 50 ft. We need the radius of this circle, so we can divide the diameter by 2 to get r = 25 ft.

Substitute this value for r into the formula for the area of a circle.

• A꜀ = π(25)²
• A꜀ = π(625)
• A꜀ = 1963.49540849 ft²

The area of the circle with a radius of 25 ft is 1963 ft².

Therefore, the circle has a greater area compared to the triangle.