57.6k views
3 votes
Learning Task 2 : Find the area of each shaded region. Assume that all angles that appear to be right triangle (3 points each).

Step by step answer
PLS

Learning Task 2 : Find the area of each shaded region. Assume that all angles that-example-1
Learning Task 2 : Find the area of each shaded region. Assume that all angles that-example-1
Learning Task 2 : Find the area of each shaded region. Assume that all angles that-example-2
User Alkindus
by
7.4k points

1 Answer

4 votes

Answer:

1. 60 ft^2

2. 175 cm^2

3. 36 cm^2

4. 121 cm^2

Explanation:

1.

First, let's find the area of the whole rectangle:

A (whole) = 7 × 12 = 84 ft^2

Then, we have to find the area of the smaller rectangle which is inside the whole rectangle:

A (smaller) = 3 × 8 = 24 ft^2

Finally, let's subtract the area of the smaller rectangle from the area of the whole rectangle and we'll get the answer:

A (shaded) = 84 - 24 = 60 ft^2

.

2.

The opposite side lengths of a rectangle are equal

First, we can find the shorter side's length of each shorter rectangle:

(16 - 9) / 2 = 3,5 cm

A shorter side of the larger rectangle would be:

16 - 9 = 7 cm

Now, we can find the area of two smaller rectangles that are on top of the larger one:

A (2 smaller rectangles) = 9 × 3,5 × 2 = 63 cm^2

Also, we have to find the area of the larger rectangle:

A (larger) = 16 × 7 = 112 cm^2

In order to find the area of the shaded region, we have to add both of these areas together:

A (shaded) = 63 + 112 = 175 cm^

.

3.

Given:

h = 12 cm

b (triangle's base) = 9 cm

a (rectangle's longer side) = 6 cm

c (rectangle's shorter side) = 3 cm

Find: A (shaded) - ?

First, let's find the area of the triangle:


a(triangle) = (1)/(2) * b * h


a(triangle) = (1)/(2) * 9 * 12 = 54 \: {cm}^(2)

Now, we have to find the area of the rectangle:


a(rectangle) = a * c = 6 * 3 = 18 \: {cm}^(2)

In order to find the area of the shaded region, we have to subtract the rectangle's area from the triangle's area:


a(shaded) = 54 - 18 = 36 \: {cm}^(2)

.

4.

Given:

r (radius) = 7 cm

a (rectangle's longer side) = 11 cm

b (rectangle's shorter side) = 3 cm

Find: A (shaded) - ?

First, let's find the area of the circle:


a(circle) = \pi {r}^(2) = \pi * {7}^(2) = 49\pi \: {cm}^(2)

Now, we have to find the area of the rectangle:


a(rectangle) = a * b = 11 * 3 = 33 \: {cm}^(2)

In order to find the shaded area, we have to subtract the rectangle's area from the circle's area:


a(shaded) = 49\pi - 33 ≈ 121 \: {cm}^(2)

User Benjamin West
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories