Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).

Question

asked Feb 24, 2020 29.1k views

2 Answers

Steboc · Answer 1 · 2020-02-27T22:52:59+0000

Answer:

The area of rectangle is
$72\ units^(2)$

Explanation:

see the attached figure with letters to better understand the problem

Let

A(3.10),B(12,1),C(16,5),D(7,14)

we know that

The area of rectangle is equal to

A=(AB)(BC)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}$

Find the distance AB

we have

A(3.10),B(12,1)

substitute in the formula

$AB=\sqrt{(1-10)^(2)+(12-3)^(2)}$

$AB=\sqrt{(-9)^(2)+(9)^(2)}$

$AB=√(162)\ units$

Find the distance BC

we have

B(12,1),C(16,5

substitute in the formula

$BC=\sqrt{(5-1)^(2)+(16-12)^(2)}$

$BC=\sqrt{(4)^(2)+(4)^(2)}$

$BC=√(32)\ units$

Find the area of rectangle

$A=(√(162))*(√(32))=72\ units^(2)$