Answer:
142.7 m²
Step-by-step explanation:
but sure, what you know about triangles and trigonometry (simplified, the relationship of angles and sides of shapes based on circles enclosing them)
so, here a quick summary of important facts and angle/side relationships in triangles :
the sum of all angles in a triangle is always and for every triangle 180 degrees.
sin(angle) is vertically up or down from the horizontal diameter of the encircling circle to the point on the circle hit by a line from the center of the circle with the described angle from the horizontal diameter.
cos(angle) is horizontally left or right from the center of the encircling circle to the point, where the sine-line hits the horizontal diameter.
the sides are named in relation to their opposing corners and their angles. so, for example, side a is opposing the corner point A and the angle at this point (also called A).
here it is also important to know :
a/sin(A) = b/sin(B) = c/sin(C)
and the area of a general triangle is
area = 1/2 × b × c × sin(A) or
1/2 × a × c × sin(B) or
1/2 × a × b × sin(C)
so, if we want to use the first option, we need to calculate b first. for this we use
b/sin(B) = c/sin(C)
b = (c × sin(B)) / sin(C)
for this we need to calculate C first. and we use
A + B + C = 180
C = 180 - A - B = 180 - 54.3 - 30.4 = 95.3 degrees
=>
b = (26.3 × sin(30.4)) / sin(95.3) = 13.36583...
=> area = 1/2 × 13.36583... × 26.3 × sin(54.3) = 142.7324...
= 142.7 (rounded)
