complete the table.
10.
11.
12.
13.
14.
15. a triangular vegetable garden is planted in the corner of a yard.
a) find the area of the garden.
b) find the area of the yard that is not planted.

Question

Accepted Answer

### Problem 10 - 14: Completing the Table (Assuming it's a parallelogram or triangle? Wait, the formula for area of a triangle is $ A=\frac{1}{2}bh $, but if it's a parallelogram, $ A = bh $. Wait, let's check the numbers. For problem 10: $ b = 4.6 $, $ h = 10 $. If it's a triangle, $ A=\frac{1}{2}\times4.6\times10 = 23 $, but maybe it's a parallelogram? Wait, problem 11: $ h = 8.4 $, $ A = 29.4 $, so $ b=\frac{A}{h}=\frac{29.4}{8.4}=3.5 $. If it's a triangle, $ b=\frac{2A}{h}=\frac{58.8}{8.4}=7 $, which is different. Wait, maybe it's a triangle? Wait, no, let's see problem 12: $ b = 6.5 $, $ h = 5.2 $, if $ A = bh $, then $ 6.5\times5.2 = 33.8 $. Problem 13: $ b = 14.4 $, $ A = 75.6 $, so $ h=\frac{75.6}{14.4}=5.25 $. Problem 14: $ h = 9.8 $, $ A = 83.3 $, so $ b=\frac{83.3}{9.8}=8.5 $. Wait, maybe it's a parallelogram (area $ A = bh $)? Let's proceed with $ A = bh $ (maybe the table is for parallelogram area).

#### Problem 10:
# Explanation:
## Step1: Identify formula (parallelogram area $ A = b \times h $)
Given $ b = 4.6 $, $ h = 10 $, so $ A = 4.6 \times 10 $
## Step2: Calculate
$ 4.6 \times 10 = 46 $
# Answer: 46

#### Problem 11:
# Explanation:
## Step1: Formula $ A = b \times h $ → $ b = \frac{A}{h} $
Given $ A = 29.4 $, $ h = 8.4 $, so $ b = \frac{29.4}{8.4} $
## Step2: Calculate
$ \frac{29.4}{8.4} = 3.5 $
# Answer: 3.5

#### Problem 12:
# Explanation:
## Step1: Formula $ A = b \times h $
Given $ b = 6.5 $, $ h = 5.2 $, so $ A = 6.5 \times 5.2 $
## Step2: Calculate
$ 6.5 \times 5.2 = 33.8 $
# Answer: 33.8

#### Problem 13:
# Explanation:
## Step1: Formula $ A = b \times h $ → $ h = \frac{A}{b} $
Given $ A = 75.6 $, $ b = 14.4 $, so $ h = \frac{75.6}{14.4} $
## Step2: Calculate
$ \frac{75.6}{14.4} = 5.25 $
# Answer: 5.25

#### Problem 14:
# Explanation:
## Step1: Formula $ A = b \times h $ → $ b = \frac{A}{h} $
Given $ A = 83.3 $, $ h = 9.8 $, so $ b = \frac{83.3}{9.8} $
## Step2: Calculate
$ \frac{83.3}{9.8} = 8.5 $
# Answer: 8.5

### Problem 15: Triangular Vegetable Garden

#### Part (a): Area of the garden (triangle)
The triangle has a base and height. From the diagram: the horizontal side of the yard is 15 m, the horizontal segment next to the triangle is 9 m, so the base of the triangle is $ 15 - 9 = 6 $ m. The vertical side of the yard is 10 m, the vertical segment next to the triangle is 4 m, so the height of the triangle is $ 10 - 4 = 6 $ m? Wait, no, wait the diagram: the triangle is in the corner, with the yard being a rectangle? Wait, the yard's length is 15 m, height is 10 m. The triangle is at the corner, with a horizontal segment of 9 m (so the base of the triangle is $ 15 - 9 = 6 $ m) and vertical segment of 4 m (so the height of the triangle is $ 10 - 4 = 6 $ m)? Wait, no, the triangle is a right triangle? Wait, the diagram shows the yard as a rectangle with length 15 m and height 10 m. The triangle is in the top-left corner, with a horizontal line of 9 m (so the base of the triangle is $ 15 - 9 = 6 $ m) and a vertical line of 4 m (so the height of the triangle is $ 10 - 4 = 6 $ m)? Wait, no, maybe the triangle's base is $ 15 - 9 = 6 $ m and height is $ 10 - 4 = 6 $ m? Wait, no, the triangle is a right triangle, so area is $ \frac{1}{2} \times \text{base} \times \text{height} $.

Wait, let's re-examine the diagram: the yard is a rectangle with length 15 m (horizontal) and height 10 m (vertical). The triangle is in the top-left corner, with a horizontal segment of 9 m (so the horizontal side of the non-triangle part is 9 m, so the base of the triangle is $ 15 - 9 = 6 $ m) and a vertical segment of 4 m (so the vertical side of the non-triangle part is 4 m, so the height of the triangle is $ 10 - 4 = 6 $ m). So the triangle has base $ 6 $ m and height $ 6 $ m? Wait, no, maybe the base is $ 15 - 9 = 6 $ m and height is $ 10 - 4 = 6 $ m? Wait, no, the triangle is a right triangle with legs equal to $ (15 - 9) $ and $ (10 - 4) $, so base $ b = 15 - 9 = 6 $ m, height $ h = 10 - 4 = 6 $ m? Wait, no, that would make the area $ \frac{1}{2} \times 6 \times 6 = 18 $ m². Wait, but maybe I misread. Wait, the diagram: the horizontal arrow is 9 m (from the triangle to the right), so the triangle's base is $ 15 - 9 = 6 $ m. The vertical arrow is 10 m (total height), and the vertical segment below the triangle is 4 m, so the triangle's height is $ 10 - 4 = 6 $ m. So area of triangle is $ \frac{1}{2} \times 6 \times 6 = 18 $ m²? Wait, no, maybe the base is $ 15 - 9 = 6 $ m and height is $ 10 - 4 = 6 $ m? Wait, let's check again.

Wait, the yard is a rectangle with length 15 m (horizontal) and width 10 m (vertical). The triangle is at the top-left corner, with a horizontal line of 9 m (so the horizontal side of the non-triangle part is 9 m, so the base of the triangle is $ 15 - 9 = 6 $ m) and a vertical line of 4 m (so the vertical side of the non-triangle part is 4 m, so the height of the triangle is $ 10 - 4 = 6 $ m). So the triangle is a right triangle with legs 6 m and 6 m. Thus, area is $ \frac{1}{2} \times 6 \times 6 = 18 $ m²? Wait, no, maybe the base is $ 15 - 9 = 6 $ m and height is $ 10 - 4 = 6 $ m? Wait, that seems correct.

# Explanation (Part a):
## Step1: Determine base and height of the triangle
Base of triangle: $ 15 - 9 = 6 $ m
Height of triangle: $ 10 - 4 = 6 $ m
## Step2: Apply triangle area formula $ A = \frac{1}{2} \times \text{base} \times \text{height} $
$ A = \frac{1}{2} \times 6 \times 6 = 18 $ m²
# Answer (a): 18 m²

#### Part (b): Area of the yard not planted
First, find the area of the yard (rectangle): $ \text{Length} \times \text{Width} = 15 \times 10 = 150 $ m²
Then, subtract the area of the garden (triangle) from the yard's area:
$ 150 - 18 = 132 $ m²

# Explanation (Part b):
## Step1: Calculate area of the yard (rectangle)
$ A_{\text{yard}} = 15 \times 10 = 150 $ m²
## Step2: Subtract garden area from yard area
$ A_{\text{not planted}} = 150 - 18 = 132 $ m²
# Answer (b): 132 m²

### Final Answers for Table (Problems 10 - 14):
10. $ 4.6 \times 10 = 46 $
11. $ \frac{29.4}{8.4} = 3.5 $
12. $ 6.5 \times 5.2 = 33.8 $
13. $ \frac{75.6}{14.4} = 5.25 $
14. $ \frac{83.3}{9.8} = 8.5 $

15. (a) 18 m²; (b) 132 m²

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 10:

Step1: Identify formula (parallelogram area \( A = b \times h \))

Step2: Calculate

Step1: Formula \( A = b \times h \) → \( b = \frac{A}{h} \)

Step2: Calculate

Step1: Formula \( A = b \times h \)

Step2: Calculate

Answer:

Problem 11: