Question

If OA = 36 and OP = 60, then the area of kite OAPB is ... .

Answer 1

Answer:

Correct answer is 1728cm²

Options are not matching because of decimal point.

Step-by-step explanation:

Given :

i) OA = 36 cm

ii) OP = 60 cm

To Find :

Area of kite OAPB

Steps to follow:

1] Find A(ΔOAP)

2] Find A(ΔOBP)

3] Add A(ΔOAP) and A(ΔOBP) = Area of kite OAPB

Solution:

STEP 1]

In ΔOAP,

∠OAP = 90° ...(Tangent theorem)

By Pythagoras' theorem,

OP² = OA²+AP²

60² = 36² + AP²

AP² = 3600 - 1296

AP² = 2304

AP = 48 ...(Taking square root of both sides)

Now,

A(ΔOAP) = 1/2 × Base × Height

= 1/2 × AP × OA

= 1/2 × 48 × 36

A(ΔOAP) = 864 cm²

STEP 2]

In ΔOAP,

∠OBP = 90° ...(Tangent theorem)

OA = OB = 36 cm ...(Radii of same circle)

By Pythagoras' theorem,

OP² = OB²+BP²

60² = 36² + BP²

BP² = 3600 - 1296

BP² = 2304

BP = 48 ...(Taking square root of both sides)

Now,

A(ΔOBP) = 1/2 × Base × Height

= 1/2 × BP × OB

= 1/2 × 48 × 36

A(ΔOBP) = 864 cm²

STEP 3]

Area of kite OAPB = A(ΔOAP) + A(ΔOBP)

= 864 + 864

= 1728 cm²

Ans. Area of kite OAPB = 1728 cm²