Question

What is the area of the unshaded region of the rectangle? part 1. Show work please​

Answer 1

Answer:

$\displaystyle 96\:m^2$

Step-by-step explanation:

You can easily solve this using Pythagorean Triplets:

$\displaystyle 3, 4, 5 \\ 6, 8, 10 \\ 9, 12, 15 \\ \boxed{12, 16, 20}$

The shorter leg is twelve metres long. Now you must find the area of this right triangle:

$\displaystyle \frac{hb}{2} = A\:OR\:\frac{1}{2}hb = A \\ \\ \frac{[16][12]}{2} = \frac{192}{2} = 96\:OR\:\frac{1}{2}[16][12] = \frac{1}{2}[192] = 96$

You see how swift that was?

I am joyous to assist you at any time.

Answer 2

Answer:

96 m²

Step-by-step explanation:

The unshaded region is a right triangle.

The area (A) of the triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

Calculate b using Pythagoras' identity in the right triangle

b² + 16² = 20²

b² + 256 = 400 ( subtract 256 from both sides )

b² = 144 ( take the square root of both sides )

b = $\sqrt{144}$ = 12

Thus area of unshaded region is

A = $\frac{1}{2}$ × 12 × 16 = 6 × 16 = 96 m²