Final answer:
To calculate the total area of two similar triangles, apply the similarity ratio to find corresponding sides and use the area formula for a triangle. In this case, the total area for both triangles is 25 cm².
Step-by-step explanation:
To find the total area for both similar triangles when the length AB = 8 cm, BC = 4 cm, and EF = 3 cm, we must first establish the similarity ratio and then use that ratio to determine the corresponding sides of the triangles and calculate their areas using the formula for the area of a triangle.
The formula for the area of a triangle is 1/2 × base × height. Given that triangle ABC is similar to another triangle (which we'll call DEF with sides DE and EF), and assuming DEF is smaller based on the given measures, we can find the similar side to BC in DEF, since EF corresponds to BC. We'll call the similar side to BC as DE.
The ratio of the sides EF to BC is 3 cm / 4 cm, which simplifies to 3/4. To find DE, we multiply AB by the ratio 3/4, getting DE = 8 cm × (3/4) = 6 cm. Now, we can find the areas of both triangles A and B.
Area of Triangle ABC (larger): 1/2 × AB × BC = 1/2 × 8 cm × 4 cm = 16 cm2
Area of Triangle DEF (smaller): 1/2 × DE × EF = 1/2 × 6 cm × 3 cm = 9 cm2
The total area of both triangles is the sum of their individual areas: 16 cm2 + 9 cm2 = 25 cm2.
Therefore, the total area for both triangles is 25 cm2.