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kicyunya [14]
3 years ago
12

What is the area of rectangle ABCD in square units ?

Mathematics
2 answers:
zloy xaker [14]3 years ago
7 0

<u><em>Answer:</em></u>

34 square units

<u><em>Explanation:</em></u>

In any rectangle, each two opposite sides are equal

<u>This means that, in the given rectangle:</u>

AB = CD and AD = BC

Area of the rectangle is the product of its dimensions (length and width)

<u>This means that:</u>

Area of ABCD = AB × BC

<u>1- getting the side length:</u>

To get the side length, we will use the distance formula:

D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

<u>For AB, we have:</u>

A = (-1,4) which means that x₁ = -1 and y₁ = 4

B = (3,3) which means that x₂ = 3 and y₂ = 3

<u>Substitute in the equation:</u>

AB = \sqrt{(3-(-1))^2+(3-4)^2} = \sqrt{17} units

<u>For BC, we have:</u>

B = (3,3) which means that x₁ = 3 and y₁ = 3

C = (1,-5) which means that x₂ = 1 and y₂ = -5

<u>Substitute in the equation:</u>

BC = \sqrt{(1-3)^2+(-5-3)^2} = 2\sqrt{17} units

<u>2- getting the area:</u>

Area of ABCD = AB × BC

Area of ABCD = \sqrt{17} *  2\sqrt{17} = 34 square units

Hope this helps :)

Licemer1 [7]3 years ago
5 0

Answer:

Step-by-step explanation:

Square units = √( 4^2 + 1^2) * √( 8^2 + 2^2)

= √17 * √68

= √1156

= 34

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