Question

1. Find the area and side length of square ACEG.

Answer 1

Answer:

$\displaystyle \rm side\: length:10\\ \rm Area: 100$

Step-by-step explanation:

we are given a square composited in a square

we want to figure out the area of the composited square

to do so we can consider Pythagoras theorem to figure out the area of the composited square remember that, Every single right angle triangle in the given figure is congruent why? see the attachment

recall Pythagoras theorem

$\displaystyle {a}^{2} + {b}^{2} = {c}^{2}$

let a and b be 6 and 8 thus

substitute:

$\displaystyle {c}^{2} = {6}^{2} + {8}^{2}$

simplify square:

$\displaystyle {c}^{2} = 36 + 64$

simplify addition:

$\displaystyle {c}^{2} = 100$

square root both sides to get the side length:

$\displaystyle {c}^{} = 10$

hence,

the area and the side length of square ACEG is 100 and 10

reference:

• the Proof is resource of our textbook

Answer 2

Square ACEG is inscribed in square BDFH, where

• The side length of ACEG is 10 units
• The area is 100 ACEG 100 squared units

Each side length of square ACEG form a right-angled triangle with the bigger square BDFH

So, the side length of ACEG is calculated by using following Pythagoras theorem.

$AG^2 = AH^2 + GH^2$

This gives:

$AG^2 = 8^2 + 6^2$

$AG^2 = 64 + 36$

$AG^2 = 100$

Take square roots

$AG = 10$

The area of the square is calculated as follows:

$Area = Length \times Length$

So, we have:

$Area = AG \times AG$

$Area = 10 \times 10$

$Area = 100$

Hence, the side length is 10 units and the area is 100 squared units

Read more about squares at:

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