Question

The white triangle is equilateral and is inscribed in a square that has sides of length 8 units. Find the area of the white triangle.

a) 16√3square units
b)24√ 2square units
c) 32√ 3square units
d) 64√2 square units

Answer 1

To find the area of the equilateral triangle inscribed in an 8-unit square, we use the Pythagorean theorem to determine the height and then apply the area formula for triangles. After calculations, the area is determined to be 16√3 square units.

Step-by-step explanation:

The question asks to find the area of an equilateral triangle inscribed in an 8-unit square. To start, the height (h) of this triangle can be determined using Pythagorean theorem, considering half the triangle as a right-angled triangle with hypotenuse as the side of the square, which also is the side of the triangle (s), and one leg being half of the side of the square (s/2).

Applying Pythagorean theorem:
h = √(s² - (s/2)²). With s = 8 units, the calculation yields h = √(64 - 16), therefore h = √(48). Simplifying, we get h = 4√3 units.

Now, the area (A) of the equilateral triangle can be found using the formula for the area of a triangle: A = 1/2 × base × height, hence A = 1/2 × 8 × 4√3 resulting in A = 16√3 square units, which is option (a).