Answer:
<h2>a. 10cm</h2><h2>b. 5 cm</h2><h2>c. 31.4 cm</h2><h2>d. 78.5 cm²</h2><h2>e. 100 cm²</h2>
Step-by-step explanation:
Let:
<em>s - </em><em>side of the square</em>
<em>d - </em><em>diameter of the circle</em>
<em>r - </em><em>radius of a circle</em>
<em>C - </em><em>circumeference of the circle</em>
<em>AC - </em><em>area of the circle</em>
<em>AS - </em><em>area of a square</em>
The formula of a perimeter of a square:
<em>P = 4s</em>
We have <em>P = 40cm.</em>
Substitute:
<em>4s = 40 </em><em>divide both sides by 4</em>
<em>s = 10 cm</em>
a.
The length of the diameter of the circle inscribed in the square is equal to the length of the side of the square.
Therefore <em>d = s → d = 10 cm.</em>
b.
The length of the circle diameter is two lengths of the circle radius.
Therefore <em>d = 2r → r = d : 2 → r = 10 : 2 = 5 cm.</em>
c.
The formula of a circumference of a circle:
<em>C = dπ.</em>
Substitute <em>d = 10cm</em>, and <em>π = 3.14.</em>
<em>C = 10(3.14) = 31.4 cm.</em>
d.
The formula of an area of a circle:
<em>AC = πr²</em>
Substitute <em>r = 5cm</em> and <em>π = 3.14</em>
<em>AC = 3.14(5²) = 3.14(25) = 78.5 cm²</em>.
e.
The formula of an area of a square:
<em>AS = s²</em>
Substitute <em>s = 10 cm</em>
<em>AS = 10² = 100 cm²</em>
