Because we do not know the height of this triangle, we need to lean into trigonometry. Luckily, Heron's Formula will help us solve this problem. You can use it when you know three sides of a triangle and want to find the area. Please note that in order to find a triangle's area, you must make sure that the triangle exists by satisfying the Triangle Inequality, which states that the sum of any two sides of the triangle must always be larger than the remaining side. This is true for the lengths 1.1, 3.7, and 4.3 given in this problem. Heron's formula can be described as:

 where R is the area of the triangle and s is the semiperimeter equivalent to . Using these formulas and plugging in, we get:

Therefore the area of  is 1.83 feet.

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 60 - 90 = 30. The pictured triangle is therefore a 30-60-90 triangle. In a 30-60-90 triangle, the ratio between the hypotenuse and the shortest side length is 2:1. Therefore, C = 2A.

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 60 - 90 = 30. The pictured triangle is therefore a 30-60-90 triangle. In a 30-60-90 triangle, the ratio between the shortest side length and the longer non-hypotenuse side length is . Therefore, .

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 60 - 90 = 30. The pictured triangle is therefore a 30-60-90 triangle. In a 30-60-90 triangle, the ratio between the hypotenuse length and the second-longest side length is . Therefore, .

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 45 - 90 = 45. The pictured triangle is therefore a 45-45-90 triangle. In a 45-45-90 triangle, the two shorter side lengths are equal. Therefore, A = B.

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 45 - 90 = 45. The pictured triangle is therefore a 45-45-90 triangle. In a 45-45-90 triangle, the ratio between a short side length and the hypotenuse is . Therefore, .

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 45 - 90 = 45. The pictured triangle is therefore a 45-45-90 triangle. In a 45-45-90 triangle, the ratio between the two short side lengths is 1:1. Therefore, A = B. Triangles with two congruent side lengths are isosceles by definition.

For any angle inscribed in a circle, the measure of the angle is equal to half of the resulting arc measure. Because  is a diameter of the circle, arc  has a measure of 180 degrees. Therefore,  must be equal to . Since  is a right triangle, the sum of its interior angles to 180 degrees. Since the measure of  is twice the measure of , . Therefore, the measure of  can be calculated as follows:

Therefore,  is equal to .  must be a 30-60-90 triangle. Therefore, side length  must be half the length of side length , the hypotenuse of the triangle. Since  is a diameter of the circle, half of  represents the length of a radius of the circle. Therefore,  is equal in length to a radius of the circle.

For any angle inscribed in a circle, the measure of the angle is equal to half of the resulting arc measure. Because  is a diameter of the circle, arc  has a measure of 180 degrees. Therefore, must be equal to . Since  is a right triangle, the sum of its interior angles equal 180 degrees. Since the measure of  is twice the measure of , . Therefore, the measure of  can be calculated as follows:

Therefore,  is equal to .  must be a 30-60-90 triangle.

Since  and  are perpendicular,  is a right angle. Since no triangle can have more than one right angle, and  is isosceles,  must be congruent to . Since  is congruent to  and  measures 90 degrees,  and  can be calculated as follows:

Therefore,    and  are both equal to 45 degrees.   is a 45-45-90 triangle. Since  is congruent to ,   is also a 45-45-90 triangle. The figure is drawn to scale, so  is a right angle. Since  has the same angle measure as , the two angles are alternate interior angles and diagonal  is a transversal relative to  and , which must be parallel.