Question

if the diagonal of square measure 25cm. find the area of the square

Answer 1

ANSWER:

• The area of the square = 312.5 cm².

GIVEN:

• The diagonal of square is of length 25 cm.

TO FIND:

• The area of the square.

DIAGRAM:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(3,0)\qbezier(0,0)(0,0)(0,3)\qbezier(0,3)(0,3)(3,3)\qbezier(3,0)(3,0)(3,3)\qbezier(0,0)(0,0)(3,3)\put(0.7,1.8){ \bf 25 \ cm }\put(-0.2,-0.3){ \bf A }\put(3,-0.3){ \bf B }\put(3.1,1.5){ \bf a }\put(-0.3,1.5){ \bf a }\put(1.5,-0.27){ \bf a }\put(1.5,3.1){ \bf a }\put(-0.2,3.1){ \bf D }\put(3.1,3){ \bf C }\end{picture}$

EXPLANATION:

Let the side of the square be a.

According to pythagoras theorem

AB² + BC² = AC²

a² + a² = 25²

2a² = 625

a² = 312.5

Area of square = a²

a² = 312.5 cm²

Hence the area if the square = 312.5 cm².

Extra Calculations:

Perimeter of the square = 4a

a² = 312.5

a = 17.68

4a = 4(17.68)

4a = 70.7 cm

Hence the perimeter of the square =70.7 cm.

Related Formulae:

Lateral surface area of cube = 6a²

Volume of cube = a³

Lateral surface area of cuboid = (l × b) + (b × h) + (l × h)

Volume if cuboid = l × b × h

C.S.A of cylinder = 2πrh

T.S.A of cylinder = 2πr(h + r)

Volume of cylinder = πr²h

C.S.A of cone = πrl

T.S.A of cone = πr(l + r)

Volume of cone = 1/3 πr²h