Alameda Post Math Puzzle for November 1, 2024

Was Heron actually a hero, and did he perform algebra?

$Alameda Post - a math diagram. A right triangle contains a circle. The circle touches all three sides of the triangle. Inside of the circle is a second, smaller triangle, and the corners of the small triangle touch the inside of the circle. The two longer sides of the internal triangle are labeled "A" and "B"$ ^[1]

Depicted above is a small scalene triangle circumscribed by a circle.
The small triangle has an area of 43 square meters.
The triangle has side A = 11 meters while side B = 12 meters.
The circle is inscribed within a 30°—60°—90° triangle.
Find the Area of the 30°—60°—90° triangle.

Area = ______ square meters

First correct answer to arrive [email protected] ^[2] will win a gift card for Tucker’s Ice Cream of Alameda, California.

Last week’s winner ^[3] was John Lovato with W = 7 in. and H = 12.12 in.

Jeff Smith is a former Math teacher and a retired US Navy Lieutenant Commander. Reach him at [email protected] ^[2].