Chapter 3: Q5. (page 150)

What is the area of the square ABCD?
(A) 27 units $^{2}$
(B) $9 \sqrt{2}$ units $^{2}$
(C) 18 units $^{2}$
(D) $12 \sqrt{2}$ units $^{2}$

Short Answer

Expert verified

The area of square ABCD is (C) 18 units².

Step by step solution

– Evaluate the length of one side of the square AB

In the graph, the points of the vertices of square are given. They are $A (- 4, 2),$ $B (- 1, 5), C (2, 2)$ and $D (- 1, 1) .$

To evaluate the length of one side, we have to evaluate the distance between two points.

The distance between two points $= \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

– Evaluate the distance between A and B

Therefore, the length of AB is

$\begin{matrix} = \sqrt{{(- 1 + 4)}^{2} + {(5 - 2)}^{2}} \\ = \sqrt{{(3)}^{2} + {(3)}^{2}} \\ = \sqrt{9 + 9} \\ = \sqrt{18} \end{matrix}$

– Evaluate the area of square ABCD

We know that all the sides of the square have same length.

Area of square $= s^{2}$

We know that $s = \sqrt{18}$ units.

Therefore, area of square ABCD is

$\begin{array}{l} = {(\sqrt{18})}^{2} \\ = \sqrt{18} \times \sqrt{18} \end{array}$

=18 units²

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What is the area of the square ABCD?
(A) 27 units $^{2}$
(B) $9 \sqrt{2}$ units $^{2}$
(C) 18 units $^{2}$
(D) $12 \sqrt{2}$ units $^{2}$

Short Answer

Step by step solution

– Evaluate the length of one side of the square AB

– Evaluate the distance between A and B

– Evaluate the area of square ABCD

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What is the area of the square ABCD?(A) 27 units 2(B)92units 2(C) 18 units 2(D)122 units 2

Short Answer

Step by step solution

– Evaluate the length of one side of the square AB

– Evaluate the distance between A and B

– Evaluate the area of square ABCD

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

What is the area of the square ABCD?
(A) 27 units $^{2}$
(B) $9 \sqrt{2}$ units $^{2}$
(C) 18 units $^{2}$
(D) $12 \sqrt{2}$ units $^{2}$