4. A regular octagon has sides measuring about 4 cm . If the octagon is divided into 8 congnuent triangles, each has a height of 5 cm . What is the area of the octagon?

To find the area of the octagon, we can use the formula for the area of a triangle and multiply it by the number of triangles. The area of one triangle is given by the formula: Area = 1/2 * base * height. Here, the base is the side length of the octagon (4 cm) and the height is 5 cm. Calculating this, we have: Area of one triangle = 1/2 * 4 cm * 5 cm = 10 cm². Since there are 8 triangles in the octagon, we multiply this area by 8: Area of the octagon = 10 cm² * 8 = 80 cm². So, the area of the regular octagon is 80 cm²! Now, just remember: if you're ever unsure about your area calculations, breaking shapes into triangles is a classic strategy. Sometimes it’s easy to overlook that the area can be determined through simpler shapes within the larger one. Being meticulous with your dimensions ensures that you get to the right answer without any drama!