Area Of Compound Shapes And Figure Quiz

Explanation
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.

Explanation
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

Explanation
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

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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:
Arearectangle=length×width
Arearectangle=15×8
Arearectangle=120 square units
Calculate the area of the square: Areasquare=side×side
Areasquare=5×5
Areasquare=25 square units
Subtract the area of the square from the area of the rectangle: Areacompound shape=Arearectangle−Areasquare
 Areacompound shape=120−25
Areacompound shape=95 square units
So, the area of the compound shape is 95 square units.

Explanation
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)
AreaRectangle 1= Height x Width
AreaRectangle 1= 9 x 8
AreaRectangle 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
AreaRectangle 2= Height x Width
AreaRectangle 2= 5x10
AreaRectangle 2= 50 square units
Add the areas of the two rectangles:
Total Area=AreaRectangle 1+AreaRectangle 2
​ Total Area=72+50
Total Area=122 square units
So, the area of the compound shape is 122 square units.

Explanation
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:
Arearectangle​=Height×Width
Arearectangle=19×6

Arearectangle=114 square units
Calculate the Area of the Right Triangle:
Areatriangle​=1/2​×Base×Height
Areatriangle= 1/2x 6x7
Areatriangle= 21
Add the Areas of the Rectangle and the Triangle:
Total Area= Arearectangle​+ Areatriangle
Total Area= 114+21
Total Area= 135 square units

Explanation
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.