Question

The box at the right is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagonal of a face, an edge, and a segment with endpoints at opposite corners of the cube. The triangle is a right triangle with leg lengths 2 and
$\sqrt{ {2}^{3} }$
. Write the area of the triangle as the number 2 with a rational exponent.​

Answer 1

Answer:

$Area = 2 \sqrt{2}$

Step-by-step explanation:

Given

$Length_1 = 2$

$Length_2 = \sqrt{2^3}$

Required

Determine the area of the triangle

The given lengths represent the height and base length of the triangle.

So, the area is;

$Area = \frac{1}{2} * Length_1 * Length_2$

Substitute values for Length1 and Length2

$Area = \frac{1}{2} * 2 * \sqrt{2^3}$

$Area = \frac{2}{2} * \sqrt{2^3}$

$Area = 1* \sqrt{2^3}$

$Area = \sqrt{2^3}$

Express 2^3 as 2 * 2 * 2

$Area = \sqrt{2*2*2}$

$Area = \sqrt{4*2}$

Split

$Area = \sqrt{4} *\sqrt{2}$

$Area = 2 *\sqrt{2}$

$Area = 2 \sqrt{2}$