Final answer:
To determine the height of the isosceles triangle, apply the Pythagorean theorem to one half of the triangle to find a height of approximately 7.746 cm. The area, using the formula 1/2 × base × height, is around 15.492 cm².
Step-by-step explanation:
Finding the Height and Area of an Isosceles Triangle
To find the height of an isosceles triangle with two sides of length 8 cm and one side of length 4 cm, imagine the triangle split down the middle to form two right-angled triangles, each with a base of 2 cm (half the length of the base of the original triangle) and a hypotenuse of 8 cm. By the Pythagorean theorem (a2 + b2 = c2), we can calculate the height (h) as follows:
h2 + 22 = 82
h2 + 4 = 64
h2 = 64 - 4
h2 = 60
h = sqrt(60)
h ≈ 7.746 cm
To find the area of the triangle, we use the formula Area = 1/2 × base × height:
Area = 1/2 × 4 cm × 7.746 cm
Area ≈ 15.492 cm2
Therefore, the height of the triangle is approximately 7.746 cm, and the area is about 15.492 cm2.