Question

the diagram shows a shaded triangle inside a rectangle. what is the area of the triangle? 24 cm² 10 cm² 11 cm² 16 cm² 32 cm² 4 cm 8 cm

Explanation:

Step1: Recall triangle area formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). For a triangle inside a rectangle where the base of the triangle is the length of the rectangle and the height is the width of the rectangle, we can use the rectangle's dimensions.

Step2: Identify base and height

From the diagram, the base of the triangle (and the length of the rectangle) is \( 8 \, \text{cm} \), and the height (and the width of the rectangle) is \( 4 \, \text{cm} \).

Step3: Calculate the area

Substitute into the formula: \( A = \frac{1}{2} \times 8 \times 4 \). First, multiply \( 8 \times 4 = 32 \), then multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times 32 = 16 \, \text{cm}^2 \). Wait, there's a mistake here. Wait, actually, another way: the area of a triangle with the same base and height as a rectangle is half the area of the rectangle. The area of the rectangle is \( 8 \times 4 = 32 \, \text{cm}^2 \), so the triangle's area is \( \frac{32}{2} = 16 \, \text{cm}^2 \)? Wait, no, wait the options have 16? Wait the options: 24, 10, 12, 16, 32? Wait the user's options: "24 cm²", "10 cm²", "12 cm²", "16 cm²", "32 cm²". Wait my calculation: base 8, height 4. \( \frac{1}{2} \times 8 \times 4 = 16 \). So the correct answer should be 16 cm².

Answer:

16 cm² (corresponding to the option with 16 cm², e.g., if the option is D. 16 cm², then D. 16 cm²)