Question

the figure shows eight congruent triangles made by dividing a square that has an area of 64 cm². what is the area of abh?
a. 20 cm²
b. 16 cm²
c. 8 cm²
d. 6 cm²
e. 4 cm²

Explanation:

Step1: Determine total triangles

The square is divided into 8 congruent triangles.

Step2: Calculate area per triangle

Total area of square is \(64 \, \text{cm}^2\). Area of one triangle (like \(ABH\)) is \(\frac{64}{8} = 8 \, \text{cm}^2\)? Wait, no—wait, looking at the figure, maybe the square is divided into 8 congruent triangles? Wait, let's re-examine. Wait, the square has area 64, so side length is 8 (since \(8\times8=64\)). Now, the triangle \(ABH\): let's see the figure. The square is divided into 8 congruent triangles? Wait, no, maybe the figure has 8 congruent triangles. Wait, the area of the square is 64, so each congruent triangle (like \(ABH\)) would have area \(64 \div 8 = 8\)? Wait, but let's check again. Wait, maybe the square is divided into 8 triangles, so each has area \(64/8 = 8\)? Wait, but let's confirm. Wait, the problem says "eight congruent triangles made by dividing a square that has an area of 64 cm²". So triangle \(ABH\) is one of the eight congruent triangles. So area of \(ABH\) is \(64 \div 8 = 8 \, \text{cm}^2\)? Wait, but wait, maybe I miscounted. Wait, let's look at the figure: points A, B, H—ABH is a triangle. The square is divided into 8 congruent triangles, so each has area \(64/8 = 8\). Wait, but the options include 8 cm² (option C). Wait, but let's check again. Wait, maybe the square is divided into 8 triangles, so area per triangle is 64/8=8. So the area of ABH is 8 cm².

Wait, no, wait—maybe the square is divided into 8 congruent triangles, so each triangle's area is 64/8=8. So the answer is 8 cm², which is option C.

Answer:

C. 8 cm²