Shaded Area Bfe93B

1. **State the problem:** We need to find the shaded area in a large right triangle with base $10$ cm and height $12$ cm, where a smaller right triangle is cut out on the left side, leaving a slanted quadrilateral (band) shaded. 2. **Identify given dimensions:** The large triangle has base $10$ cm and height $12$ cm (sum of $2$ cm and $10$ cm for base segments, and $2$ cm and $8$ cm for height segments). 3. **Calculate the area of the large triangle:** $$\text{Area}_{\text{large}} = \frac{1}{2} \times 10 \times 12 = 60 \text{ cm}^2$$ 4. **Calculate the area of the smaller cut-out triangle:** The smaller triangle has base $2$ cm and height $2$ cm. $$\text{Area}_{\text{small}} = \frac{1}{2} \times 2 \times 2 = 2 \text{ cm}^2$$ 5. **Calculate the shaded area:** The shaded area is the large triangle area minus the small triangle area. $$\text{Area}_{\text{shaded}} = 60 - 2 = 58 \text{ cm}^2$$ 6. **Answer:** The shaded area is $58$ square centimeters.