To calculate the height of the triangle with a given area of 15.3 cm² and a base of 4.5 cm, you apply the formula A = ½ × base × height, rearrange it to solve for the height, and then perform the appropriate calculations, resulting in a height of 6.8 cm.
Step-by-step explanation:
To find the height, h, of a triangle with an area A of 15.3 square centimeters and a base b of 4.5 centimeters, we use the formula for the area of a triangle: A = ½ × base × height. Inserting the known values into the equation, we get:
15.3 cm² = ½ × 4.5 cm × h
To solve for h, we first multiply both sides by 2 to eliminate the fraction:
30.6 cm² = 4.5 cm × h
Next, we divide both sides by the base, 4.5 cm, to find the height:
h = 30.6 cm² ÷ 4.5 cm
h = 6.8 cm
So the height of the triangle is 6.8 centimeters