Question

find the area of the shaded triangle in each diagram.
1.
20 cm
15 cm
2.
20 cm
5 cm 10 cm
3.
20 cm
10 cm
15 cm
4.
7.5 cm
20 cm
calculate the area of each triangle.
5.
3 cm
9 cm
a =
6.
11 cm
12.2 cm
a =
7.
4.5 cm
7.8 cm
a =

Explanation:

Step1: Recall Triangle Area Formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Solve Problem 1

• Base: 15 cm, Height: 20 cm.
• \( A = \frac{1}{2} \times 15 \times 20 = 150 \, \text{cm}^2 \).

Step3: Solve Problem 2

• Base: \( 5 + 10 = 15 \, \text{cm} \), Height: 20 cm.
• \( A = \frac{1}{2} \times 15 \times 20 = 150 \, \text{cm}^2 \).

Step4: Solve Problem 3

• Base: 15 cm, Height: 10 cm.
• \( A = \frac{1}{2} \times 15 \times 10 = 75 \, \text{cm}^2 \).

Step5: Solve Problem 4

• Base: 20 cm, Height: 7.5 cm.
• \( A = \frac{1}{2} \times 20 \times 7.5 = 75 \, \text{cm}^2 \).

Step6: Solve Problem 5

• Base: 9 cm, Height: 3 cm.
• \( A = \frac{1}{2} \times 9 \times 3 = 13.5 \, \text{cm}^2 \).

Step7: Solve Problem 6

• Base: 12.2 cm, Height: 11 cm.
• \( A = \frac{1}{2} \times 12.2 \times 11 = 67.1 \, \text{cm}^2 \).

Step8: Solve Problem 7

• Base: 7.8 cm, Height: 4.5 cm.
• \( A = \frac{1}{2} \times 7.8 \times 4.5 = 17.55 \, \text{cm}^2 \).

Answer:

1. \( 150 \, \text{cm}^2 \)
2. \( 150 \, \text{cm}^2 \)
3. \( 75 \, \text{cm}^2 \)
4. \( 75 \, \text{cm}^2 \)
5. \( 13.5 \, \text{cm}^2 \)
6. \( 67.1 \, \text{cm}^2 \)
7. \( 17.55 \, \text{cm}^2 \)