Question

The length of the base of the triangle is 6x -2 meters, the height of the triangle is (3x+2)². find the algebraic expression of the area of the triangle (area=bxh/2)

Answer 1

• 27x³ + 27x² - 4 meters²

Step-by-step explanation:

To find the area of the triangle, we must multiply 1/2 x base x altitude to get the answer. But first, we need to simplify the height. We are given the base and the altitude.

• Base = 6x - 2
• Height = (3x + 2)²

Solution:

• Area of triangle = 1/2 x (6x - 2) x (3x + 2)²
• => Area of triangle = 1/2 x (6x - 2) x (3x + 2)(3x + 2)
• => Area of triangle = 1/2 x (6x - 2) x (3x + 2)(3x + 2)
• => Area of triangle = 1/2 x (6x - 2) x (9x² + 6x + 6x + 4)
• => Area of triangle = 1/2 x (6x - 2) x (9x² + 12x + 4)
• => Area of triangle = 1/2 x (54x³ - 18x² + 72x² - 24x + 24x - 8)
• => Area of triangle = 1/2 x (54x³ + 54x² - 8)
• => Area of triangle = (54x³/2 + 54x²/2 - 8/2)
• => Area of triangle = 27x³ + 27x² - 4 meters²

Hence, the area of the triangle is 27x³ + 27x² - 4 meters².