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. 18 cm² c. 8 cm² d. 6 cm² e. 4 cm²

Explanation:

Step1: Understand the square's area

The square has an area of \( 64 \, \text{cm}^2 \). It is divided into 8 congruent triangles.

Step2: Calculate the area of one triangle

To find the area of one triangle (like \( \triangle ABH \)), we divide the total area of the square by the number of congruent triangles. So, the area of one triangle is \( \frac{64}{8} = 8 \, \text{cm}^2 \)? Wait, no, wait. Wait, looking at the figure, maybe I miscounted. Wait, the square is divided into 8 congruent triangles? Wait, let's check again. Wait, the square is split into smaller regions. Wait, actually, the square's area is 64, and if there are 8 congruent triangles, then each triangle's area is \( 64 \div 8 = 8 \)? But wait, maybe I made a mistake. Wait, no, let's see the figure. The square is divided into 8 congruent triangles? Wait, no, maybe 8 congruent triangles? Wait, the square has area 64, so side length is \( \sqrt{64} = 8 \, \text{cm} \). Now, looking at triangle \( ABH \), let's see the dimensions. \( AB \) and \( AH \): since the square is divided into smaller squares or rectangles? Wait, maybe the square is divided into 8 congruent right triangles. So each triangle's area is \( 64 \div 8 = 8 \)? But wait, the options have 8 as option C? Wait, no, wait, maybe I miscounted. Wait, no, let's re-express. Wait, the square is divided into 8 congruent triangles, so area of each is \( 64/8 = 8 \). But wait, option C is 8, but wait, maybe I made a mistake. Wait, no, let's check again. Wait, the square's area is 64, divided into 8 congruent triangles, so each triangle's area is \( 64 \div 8 = 8 \, \text{cm}^2 \). So the area of \( \triangle ABH \) is 8? But wait, option C is 8, but wait, maybe the figure is different. Wait, no, maybe the square is divided into 16 small triangles? No, the problem says eight congruent triangles. So \( 64 \div 8 = 8 \). So the area is 8? But wait, option C is 8, but wait, let's check the options. Wait, the options are A.20, B.18, C.8, D.6, E.4. So maybe the correct answer is C? Wait, no, wait, maybe I made a mistake. Wait, the square is divided into 8 congruent triangles, so each has area 8. So the area of \( ABH \) is 8. So answer is C? Wait, but let's confirm. Wait, the square's area is 64, 8 congruent triangles, so each is 8. So yes, the area of \( \triangle ABH \) is \( 8 \, \text{cm}^2 \).

Answer:

C. \( 8 \, \text{cm}^2 \)