לפניכם מנסרות ישרות שבסיסן משולשים שוויי-צלעות שאינם ישרים זוויות. האורכים הם בס"מ. היעזרו בנתון לגבי גובה הבסיס AB, וחשו את שטח הפנים של כל מנסרה:

א. Step 1: Calculate the area of the base triangle. The diagram for part a shows a right-angled triangle with legs $5 \text{ cm}$ and $7 \text{ cm}$. We will proceed with this interpretation, assuming the general description "isosceles triangles that are not right-angled" does not apply to this specific diagram. The height of the prism is $AB = 6 \text{ cm}$. $A_{base} = \frac{1}{2} \times leg_1 \times leg_2 = \frac{1}{2} \times 5 cm \times 7 cm = 17.5 cm^2$

Step 2: Calculate the perimeter of the base triangle. First, find the hypotenuse $c$ using the Pythagorean theorem. $c = \sqrt{5^2 + 7^2} = \sqrt{25 + 49} = \sqrt{74} \text{ cm}$ $P_{base} = 5 cm + 7 cm + \sqrt{74} cm = (12 + \sqrt{74}) \text{ cm}$

Step 3: Calculate the total surface area of the prism. The height of the prism is $h_{prism} = AB = 6 \text{ cm}$. The total surface area is $A_{total} = 2 \times A_{base} + P_{base} \times h_{prism}$. $A_{total} = 2 \times 17.5 cm^2 + (12 + \sqrt{74}) cm \times 6 \text{ cm}$ $A_{total} = 35 cm^2 + (72 + 6\sqrt{74}) cm^2$ $A_{total} = (107 + 6\sqrt{74}) cm^2$ Using $\sqrt{74} \approx 8.6023$: $A_{total} \approx 107 + 6 \times 8.6023 cm^2 \approx 107 + 51.6138 cm^2 \approx 158.61 cm^2$ The total surface area for prism a is $\boxed{*(107 + 6\sqrt{74}) cm^2 \approx 158.61 cm^2*}$.

ב. Step 1: Calculate the area of the base triangle. The base is an isosceles triangle with sides $13 \text{ cm}$, $13 \text{ cm}$, and $10 \text{ cm}$. The height of the prism is $AB = 12 \text{ cm}$. To find the height of the triangle ($h_{base}$), we bisect the base of $10 \text{ cm}$ into two $5 \text{ cm}$ segments. $h_{base}^2 + 5^2 = 13^2$ $h_{base}^2 + 25 = 169$ $h_{base}^2 = 144$ $h_{base} = 12 \text{ cm}$ $A_{base} = \frac{1}{2} \times base \times h_{base} = \frac{1}{2} \times 10 cm \times 12 cm = 60 cm^2$

Step 2: Calculate the perimeter of the base triangle. $P_{base} = 13 cm + 13 cm + 10 cm = 36 \text{ cm}$

Step 3: Calculate the total surface area of the prism. The height of the prism is $h_{prism} = AB = 12 \text{ cm}$. $A_{total} = 2 \times A_{base} + P_{base} \times h_{prism}$ $A_{total} = 2 \times 60 cm^2 + 36 cm \times 12 \text{ cm}$ $A_{total} = 120 cm^2 + 432 cm^2$ $A_{total} = 552 cm^2$ The total surface area for prism b is $\boxed{*552 cm^2*}$.

ג. Step 1: Calculate the area of the base triangle. The base is an isosceles triangle with sides $26 \text{ cm}$, $26 \text{ cm}$, and $20 \text{ cm}$. The height of the prism is $AB = 24 \text{ cm}$. To find the height of the triangle ($h_{base}$), we bisect the base of $20 \text{ cm}$ into two $10 \text{ cm}$ segments. $h_{base}^2 + 10^2 = 26^2$ $h_{base}^2 + 100 = 676$ $h_{base}^2 = 576$ $h_{base} = 24 \text{ cm}$ $A_{base} = \frac{1}{2} \times base \times h_{base} = \frac{1}{2} \times 20 cm \times 24 cm = 240 cm^2$

Step 2: Calculate the perimeter of the base triangle. $P_{base} = 26 cm + 26 cm + 20 cm = 72 \text{ cm}$

Step 3: Calculate the total surface area of the prism. The height of the prism is $h_{prism} = AB = 24 \text{ cm}$. $A_{total} = 2 \times A_{base} + P_{base} \times h_{prism}$ $A_{total} = 2 \times 240 cm^2 + 72 cm \times 24 \text{ cm}$ $A_{total} = 480 cm^2 + 1728 cm^2$ $A_{total} = 2208 cm^2$ The total surface area for prism c is $\boxed{*2208 cm^2*}$.