Question

$\huge \mathfrak \pink{ Question} \huge \: \star$
Find the difference in the areas of two square one with the length of side 3.5 cm. and other with the length of a diagonal 7cm.

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Answer 1

Given:

• Square A has side 3.5cm
• Square B has the diagonal 7cm

To Find:

• the difference in their areas

Solution:

✏ now let's find the area of the first square

In the case of the first square the measure of the side is given.

$\sf{ \underbrace{ \red{area \: of \: a \: square = side \times side}}}$

Now let's substitute the given values

$\\ { : \implies} \sf \: area \: of \: the \: square = 3.5 \times 3.5 \\ \\ \\ \\ { : \implies} \sf \: area \: of \: the \: square = {3.5}^{2} \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: area \: of \: the \: square = { \purple{ \underline{\boxed{ \sf 12.25 {cm}^{2} }}}} \bigstar$

Now let's find the area of the square second square

✏ here the given measurements are of diagonal

$\sf {\underbrace{ \red{area \: of \: square = \frac{1}{2} \times {diagonal}^{2} }}}$

let's substitute the given values now:

$\\ \\ { : \implies} \sf \: area \: of \: the \: square = \frac{1}{2} \times {7}^{2} \\ \\ \\ { : \implies} \sf \: area \: of \: the \: square = \frac{1}{2} \times49 \\ \\ \\ { : \implies} \sf \: area \: of \: the \: square ={ \purple{ \underline{ \boxed{ \sf{ 24.50}}}}} \bigstar$

❍ Now let's find the difference:

$\\ : \longrightarrow \sf \pink{ area_{1} - area_{2}} = difference \: \: \: \: \: \: \: \: \: \\ \\ \\ : \longrightarrow \sf \pink{24.5 {m}^{2} - 12.25 {m}^{2} } = difference \\ \\ \\ : \longrightarrow \sf \: difference = { \underline{\boxed{ \sf12.25 {m}^{2} }}} \bigstar \: \: \: \: \: \: \: \:$

Knowledge Square:

$\leadsto \sf \: area \: of \: a \: triangle = \frac{1}{2} b \times h \\ \\ \leadsto \sf \: area \: of \: a \: circle = \pi \: {r}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \leadsto \sf \: area \: of \: a \: rectangle = l \times b \:\: \: \: \: \: \: \\ \\ \leadsto \sf \: area \: of \: a \: parallelogram = b \times h$

Answer 2

Answer: 3.5 cm is the answer