1. **State the problem:** We need to find the total area of a kite made of two pieces of fabric sewn together at the midpoint of the base. 2. **Given data:** - Base of one piece of fabric = 25 units - Angle at the top of this piece = 31° - Angle at the corner not sewn to the other fabric = 42° 3. **Understanding the kite:** The kite is symmetric, and the two pieces meet at the midpoint of the base, so the total base of the kite is twice 25, i.e., 50 units. 4. **Formula for area of kite:** The area of a kite can be found by splitting it into two triangles and summing their areas. Area of a triangle = $$\frac{1}{2}ab\sin(C)$$ where $a$ and $b$ are sides and $C$ is the included angle. 5. **Calculate the height of the piece with base 25:** Using the angle 31°, the height $h$ can be found by: $$h = 25 \times \tan(31^\circ)$$ Calculate: $$h = 25 \times 0.6009 = 15.0225$$ 6. **Calculate the area of one piece:** Area = $$\frac{1}{2} \times 25 \times 15.0225 = 187.78$$ 7. **Calculate the area of the other piece:** The other piece has the same base 25 and angle 42°. Height $h_2$: $$h_2 = 25 \times \tan(42^\circ) = 25 \times 0.9004 = 22.51$$ Area of second piece: $$\frac{1}{2} \times 25 \times 22.51 = 281.38$$ 8. **Total area of kite:** $$187.78 + 281.38 = 469.16$$ **Final answer:** The total area of the kite is approximately $469.16$ square units.