Question

find the area of the shaded triangle in each diagram.
1.
2.
3.
4.
calculate the area of each triangle.
5.
6.
7.
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Explanation:

1. Step1: Identify base and height

The shaded triangle is in a rectangle with length 15 cm (base of triangle) and height 20 cm (height of triangle).

1. Step2: Apply triangle area formula

Area of triangle $A = \frac{1}{2} \times base \times height = \frac{1}{2} \times 15 \times 20 = 150 \, cm^2$

2. Step1: Find base of triangle

Total base of rectangle is $5 + 10 = 15 \, cm$ (base of triangle), height is 20 cm.

2. Step2: Calculate area

$A = \frac{1}{2} \times 15 \times 20 = 150 \, cm^2$ (Wait, no, wait: Wait, the base here: Wait, the shaded triangle's base is the sum of 5 and 10? Wait, no, the rectangle's length is 5 + 10 = 15, so base of triangle is 15, height 20. Wait, but maybe I misread. Wait, the second diagram: the base of the triangle is 5 + 10 = 15? Wait, no, the triangle's base is the length of the rectangle, which is 5 + 10 = 15, height 20. So area is $\frac{1}{2} \times 15 \times 20 = 150$? Wait, no, maybe the base is 5 + 10 = 15, yes. Wait, but let's check again.

Wait, maybe the first diagram: the rectangle is 15 cm (width) and 20 cm (height). The shaded triangle has base 15 and height 20. So area $\frac{1}{2} \times 15 \times 20 = 150 \, cm^2$.

Second diagram: the base of the triangle is 5 + 10 = 15 cm, height 20 cm. So area $\frac{1}{2} \times 15 \times 20 = 150 \, cm^2$? Wait, no, maybe the base is 5 + 10 = 15, yes.

Third diagram: The rectangle is 15 cm (width) and 20 cm (height). The shaded triangle is at the top, with base 15 cm and height (20 - 10)? Wait, no, the diagram shows the rectangle has height 20, and the distance from the triangle to the bottom is 10? Wait, no, the third diagram: the rectangle is 15 cm (width) and 20 cm (height). The shaded triangle is at the top, with base 15 cm and height (20 - 10)? Wait, no, the vertical arrow is 10 cm, so the height of the triangle is 10 cm? Wait, maybe I misread. Wait, the third diagram: the rectangle is 15 cm (width) and 20 cm (height). The shaded triangle is at the top, with base 15 cm and height 10 cm? Wait, no, the vertical arrow is 10 cm, so the height of the triangle is 10 cm. So area $\frac{1}{2} \times 15 \times 10 = 75 \, cm^2$.

Fourth diagram: The rectangle is 20 cm (width) and 7.5 cm (height)? Wait, no, the height of the rectangle is 7.5? Wait, the diagram shows 20 cm (width) and 7.5 cm (height). The shaded triangle is at the top, with base 20 cm and height 7.5 cm? Wait, no, the height of the triangle is 7.5 cm. So area $\frac{1}{2} \times 20 \times 7.5 = 75 \, cm^2$.

Fifth diagram: Right triangle with legs 3 cm and 9 cm. Area $\frac{1}{2} \times 3 \times 9 = 13.5 \, cm^2$.

Sixth diagram: Triangle with base 12.2 cm and height 11 cm. Area $\frac{1}{2} \times 12.2 \times 11 = 67.1 \, cm^2$.

Seventh diagram: Triangle with base 7.8 cm and height 4.5 cm. Area $\frac{1}{2} \times 7.8 \times 4.5 = 17.55 \, cm^2$.

Wait, let's redo each:

1. Diagram 1:
- Rectangle: width = 15 cm (base of triangle), height = 20 cm (height of triangle)
- Area of triangle: $\frac{1}{2} \times 15 \times 20 = 150 \, cm^2$

2. Diagram 2:
- Base of triangle: 5 + 10 = 15 cm, height = 20 cm
- Area: $\frac{1}{2} \times 15 \times 20 = 150 \, cm^2$

3. Diagram 3:
- Base of triangle: 15 cm, height = 10 cm (from the diagram, the vertical segment is 10 cm)
- Area: $\frac{1}{2} \times 15 \times 10 = 75 \, cm^2$

4. Diagram 4:
- Base of triangle: 20 cm, height = 7.5 cm
- Area: $\frac{1}{2} \times 20 \times 7.5 = 75 \, cm^2$

5. Diagram 5:
- Right triangle, legs 3 cm and 9 cm
- Area: $\frac{1}{2} \times 3 \times 9 = 13.5 \, cm^2$

6. Diagram 6:
- Base = 12.2 cm, height = 11 cm
- Area: $\frac{1}{2} \times 12.2 \times 11 = 67.1 \, cm^2$

7. Diagram 7:
- Base = 7.8 cm, height = 4.5 cm
- Area: $\frac{1}{2} \times 7.8 \times 4.5 = 17.55 \, cm^2$

Answers:

1. $150 \, cm^2$
2. $150 \, cm^2$ (Wait, maybe I made a mistake here. Wait, the second diagram: the base of the triangle is 5 + 10 = 15? Or is the base 5 + 10 = 15? Wait, the rectangle's length is 5 + 10 = 15, so the triangle's base is 15, height 20. So area is 150.
3. $75 \, cm^2$
4. $75 \, cm^2$
5. $13.5 \, cm^2$
6. $67.1 \, cm^2$
7. $17.55 \, cm^2$

Answer:

s:

1. $150 \, cm^2$
2. $150 \, cm^2$ (Wait, maybe I made a mistake here. Wait, the second diagram: the base of the triangle is 5 + 10 = 15? Or is the base 5 + 10 = 15? Wait, the rectangle's length is 5 + 10 = 15, so the triangle's base is 15, height 20. So area is 150.
3. $75 \, cm^2$
4. $75 \, cm^2$
5. $13.5 \, cm^2$
6. $67.1 \, cm^2$
7. $17.55 \, cm^2$