Question 1183546
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In the diagram shown in the image, ⊙A is tangent to ⊙C, and BD is tangent to ⊙A. 
The radius of ⊙A is 7 meters, and the radius of ⊙C is 4 meters. 
What is the area, to the nearest square centimeter, of △ADB? 
Here is a link to the image: https://imgur.com/a/WQnYGaB
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<pre>
Triangle ADB is a right-angled triangle.


Its leg AB has the length of 7 meters;  its hypotenuse is  AD = 7 + 4 + 4 = 15 meters.


HENCE, its other leg is  {{{sqrt(15^2 - 7^2)}}} = {{{sqrt(225-49)}}} = {{{sqrt(176)}}} = {{{4*sqrt(11)}}}.


The area of this right-angled triangle is half the product of its legs


    area = {{{(1/2)*7*4*sqrt(11)}}} = {{{7*2*sqrt(11)}}} = {{{14*sqrt(11)}}} = 46.43274706 square meters.    <U>ANSWER</U>
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Solved and explained.