Shown below on the left are two wooden pieces joined together. The joint wooden block is cut at two places AA and BB at 45-degree angles respectively as shown in the enlarged figure on the right. Calculate the area shaded in black. Give your answer in square cm.
Show Hint
When calculating the area of a right-angled triangle, use the formula \( \frac{1}{2} \times \text{Base} \times \text{Height} \).
Step 1: Understanding the Geometry.
The joint wooden block has dimensions 12 cm by 7 cm, with cuts at 45-degree angles at points AA and BB. The shaded area is the triangular region formed by these cuts.
Step 2: Area of the Shaded Triangle.
The base of the triangle is 12 cm, and the height is 7 cm. Since the triangle is right-angled, the area is given by:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 12 \, \text{cm} \times 7 \, \text{cm} = 42 \, \text{cm}^2.
\]
\[
\boxed{42 \, \text{cm}^2}
\]
