Area Of Compound Shapes And Figure Quiz

To find the area of the parallelogram shown in the image, you can use the formula for the area of a parallelogram:

Area=base×height

In this case, the base of the parallelogram is 15 units and the height is 10 units.

Area=15×10

Area=150

So, the area of the parallelogram is 150 square units.

To find the area of the rectangle shown in the image, we use the formula for the area of a rectangle, which is:

Area=length×width

Given that the length of the rectangle is 8 units and the width is 5 units, we can calculate the area as follows:

Area=8×5=40 square units

So, the area of the rectangle is 40 square units.

To find the area of the square shown in the image, we use the formula for the area of a square, which is:

Area=side×side

Given that each side of the square is 4 units, we can calculate the area as follows:

Area=4×4=16 square units

So, the area of the square is 16 square units.

To find the area of the triangle shown in the new image, you can again use the formula for the area of a triangle:

Area=1/2×base×height

In this case, the base of the triangle is 13 units and the height is 6 units.

Area=1/2×13×6

Area=1/2​×78

Area=39

So, the area of the triangle is 39 square units.

To find the area of a parallelogram, you use the formula:

Area=base×height

Given:

The base of the parallelogram is 6 units.

The height of the parallelogram is 6 units.

Plugging in these values:

Area=6 units×6 units=36 square units

So, the area of the parallelogram is 60 square units

To find the area of the triangle shown in the image, you can use the formula for the area of a right triangle, which is:

Area=1/2×base×height

In this case, the base of the triangle is 13 units and the height is 7 units.

Area=1/2×13×7

Area=1/2×91

Area=45.5

So, the area of the triangle is 45.5 square units.

To find the area of the trapezium (trapezoid) shown in the image, you can use the formula for the area of a trapezoid:

Area=1/2×(base₁+base₂)×height

In this case, the lengths of the two bases are 15 units and 25 units, and the height is 16 units.

Area=1/2×(15+25)×16

Area=1/2×40×16

Area=20×16

Area=320

So, the area of the trapezium is 320 square units.

To find the area of the triangle shown in the image, we can use the formula for the area of a triangle:

Area=1/2×base×height

Given that the base of the triangle is 17 units and the height is 4 units, we can calculate the area as follows:

Area=1/2×17×4

Area=1/2×68

Area=34 square units

So, the area of the triangle is 34 square units.

The compound shape consists of a large rectangle and a right triangle on the right.

Dimensions:

Rectangle:

Height: 19 units

Width: 6 units

Right Triangle:

Base: 6 units

Height: 7 units (since the total height of the shape is 19 units, and the height of the rectangle part is 12 units, the remaining height is 7 units)

Calculate the Area of the Rectangle:

Area_rectangle​=Height×Width

Area_rectangle=19×6

Area_rectangle=114 square units

Calculate the Area of the Right Triangle:

Area_triangle​=1/2​×Base×Height

Area_triangle= 1/2x 6x7

Area_triangle= 21

Add the Areas of the Rectangle and the Triangle:

Total Area= Area_rectangle​+ Area_triangle

Total Area= 114+21

Total Area= 135 square units

Let's break down the shape into two rectangles in a detailed manner to find the total area.

Identify the dimensions:

The total width of the larger rectangle is 18 units.

The height of the larger rectangle is 9 units.

The height of the smaller cut-out rectangle is 4 units.

The width of the smaller cut-out rectangle is 10 units.

Divide the shape into two rectangles:

Rectangle 1: The left part of the shape.

Rectangle 2: The right part of the shape excluding the cut-out part.

Calculate the area of Rectangle 1:

Rectangle 1 has the full height and part of the width:

Height = 9 units

Width = 8 units (18 - 10)

Area_Rectangle 1= Height x Width

Area_Rectangle 1= 9 x 8

Area_Rectangle 1= 72 square units



Calculate the area of Rectangle 2:

Rectangle 2 includes the remaining part of the shape:

Height = 5 units (9 - 4)

Width = 10 units

Area_{Rectangle 2}= Height x Width

Area_{Rectangle 2}= 5x10

Area_{Rectangle 2}= 50 square units

Add the areas of the two rectangles:

Total Area=Area_Rectangle 1+Area_{Rectangle 2}

​ Total Area=72+50

Total Area=122 square units

So, the area of the compound shape is 122 square units.

To find the area of the compound shape (an orange rectangle with a white square cut out of it), you need to calculate the area of the rectangle and then subtract the area of the square.

Calculate the area of the rectangle:

Area_rectangle=length×width

Area_rectangle=15×8

Area_rectangle=120 square units

Calculate the area of the square: Area_square=side×side

Area_square=5×5

Area_square=25 square units

Subtract the area of the square from the area of the rectangle: Area_{compound shape}=Area_rectangle−Area_square

 Area_{compound shape}=120−25

Area_{compound shape}=95 square units

So, the area of the compound shape is 95 square units.

Identify the sides:

Hypotenuse (c) = 16 units

Base (b) = 4 units

Use the Pythagorean theorem:

For a right triangle with sides a (height), b (base), and c (hypotenuse), the Pythagorean theorem states:

a²+b²=c²

Plug in the values:

a²+4²=16²

a² + 16 = 256

a²=256−16

a=√240

Simplify √240:

√240 = √16x15

√240= 4√15

Calculate the area: The area A of a right triangle is given by:

A=1/2×base×height

Plugging in the values:

A=1/2x4x4√15

A=8√15

Calculate the area of the entire rectangle:

Length = 13 units (7 + 4 + 2)

Width = 5 units

Area of rectangle = Length × Width = 13 × 5 = 65 square units

Calculate the area of the triangles to be subtracted:

There are two triangles with base = 2 units and height = 5 units.

Area of one triangle = 1/2 × base × height = 1/2 × 2 × 5 = 5 square units

Total area of both triangles = 5 + 5 = 10 square units

Subtract the area of the triangles from the rectangle:

Area of the compound shape = Area of rectangle - Area of triangles

Area of the compound shape = 65 - 10 = 55 square units

Therefore, the area of the compound shape is 55 square units.