Perimeter (km) Length of rectangle (km) Width of rectangle (km) Area of protected region ( k m 2 ) 20 1 20 2 20 20 20 5 20 20 20 9 . 8 Calculate the area with other values of the perimeter. Which shape seems to maximize the area of the protected region?

Take any value to find the area of protected region. Area of rectangle = l × b Perimeter of rectangle = 2 ( l + b ) Perimeter is constant i.e 20 k m Now, 1 If L = 1 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 1 + b ⇒ 20 = 2 + 2 b ⇒ 20 - 2 2 = b ⇒ 9 = b Area of protected region = l × b = 1 × 9 = 9 k m 2 2 If L = 2 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 2 + b ⇒ 20 = 4 + 2 b ⇒ 20 - 4 2 = b ⇒ 8 = b Area of protected region = l × b = 2 × 8 = 16 k m 2 3 If L = 3 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 3 + b ⇒ 20 = 6 + 2 b ⇒ 20 - 6 2 = b ⇒ 7 = b Area of protected region = l × b = 3 × 7 = 21 k m 2 4 If L = 4 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 4 + b ⇒ 20 = 8 + 2 b ⇒ 20 - 8 2 = b ⇒ 6 = b Area of protected region = l × b = 4 × 6 = 24 k m 2 5 If L = 5 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 5 + b ⇒ 20 = 10 + 2 b ⇒ 20 - 10 2 = b ⇒ 5 = b Area of protected region = l × b = 5 × 5 = 25 k m 2 6 If L = 6 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 6 + b ⇒ 20 = 12 + 2 b ⇒ 20 - 12 2 = b ⇒ 4 = b Area of protected region = l × b = 6 × 4 = 24 k m 2 7 If L = 7 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 7 + b ⇒ 20 = 14 + 2 b ⇒ 20 - 14 2 = b ⇒ 3 = b Area of protected region = l × b = 7 × 3 = 21 k m 2 6 If L = 9 . 8 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 9 . 8 + b ⇒ 20 = 19 . 6 + 2 b ⇒ 20 - 19 . 6 2 = b ⇒ 0 . 2 = b Area of protected region = l × b = 9 . 8 × 0 . 2 = 1 . 96 k m 2 Perimeter (km) Length of rectangle (km) Width of rectangle (km) Area of protected region ( k m 2 ) 20 1 9 9 20 2 8 16 20 3 7 21 20 4 6 24 20 5 5 25 20 6 8 16 20 7 3 21 20 9 . 8 0 . 2 1 . 96 Area of protected region will maximize when length and breadth both will be 5 k m

Perimeter (km) Length of rectangle (km) Width of rectangle (km) Area of protected region ( k m 2 ) 20 1 20 2 20 20 20 5 20 20 20 9 . 8 Write down a generalization about the relationship between the area of a rectangle and its perimeter , when the perimeter remains constant.

Take any value and find the area of protected region. Area of rectangle = l × b Perimeter of rectangle = 2 ( l + b ) Perimeter is constant i.e 20 k m Now, 1 If L = 1 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 1 + b ⇒ 20 = 2 + 2 b ⇒ 20 - 2 2 = b ⇒ 9 = b Area of protected region = l × b = 1 × 9 = 9 k m 2 2 If L = 2 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 2 + b ⇒ 20 = 4 + 2 b ⇒ 20 - 4 2 = b ⇒ 8 = b Area of protected region = l × b = 2 × 8 = 16 k m 2 3 If L = 3 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 3 + b ⇒ 20 = 6 + 2 b ⇒ 20 - 6 2 = b ⇒ 7 = b Area of protected region = l × b = 3 × 7 = 21 k m 2 4 If L = 4 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 4 + b ⇒ 20 = 8 + 2 b ⇒ 20 - 8 2 = b ⇒ 6 = b Area of protected region = l × b = 4 × 6 = 24 k m 2 5 If L = 5 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 5 + b ⇒ 20 = 10 + 2 b ⇒ 20 - 10 2 = b ⇒ 5 = b Area of protected region = l × b = 5 × 5 = 25 k m 2 6 If L = 6 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 6 + b ⇒ 20 = 12 + 2 b ⇒ 20 - 12 2 = b ⇒ 4 = b Area of protected region = l × b = 6 × 4 = 24 k m 2 7 If L = 7 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 7 + b ⇒ 20 = 14 + 2 b ⇒ 20 - 14 2 = b ⇒ 3 = b Area of protected region = l × b = 7 × 3 = 21 k m 2 6 If L = 9 . 8 k m Perimeter = 2 ( l + b ) ⇒ 20 = 2 9 . 8 + b ⇒ 20 = 19 . 6 + 2 b ⇒ 20 - 19 . 6 2 = b ⇒ 0 . 2 = b Area of protected region = l × b = 9 . 8 × 0 . 2 = 1 . 96 k m 2 Perimeter (km) Length of rectangle (km) Width of rectangle (km) Area of protected region ( k m 2 ) 20 1 9 9 20 2 8 16 20 3 7 21 20 4 6 24 20 5 5 25 20 6 8 16 20 7 3 21 20 9 . 8 0 . 2 1 . 96 The area is the region covered by shape or figure whereas perimeter is the distance covered by outer boundary of the shape. From the table we found out that rectangles that have the same perimeter don't necessarily have the same area.

EASY

MYP:1

IMPORTANT

Earn 100

Complete the below table. Round number to the nearest hundredth where appropriate.

Triangle's base in (cm) Triangle's height in (cm) Triangle's area in (square cm)

$10$ $12.6$

50% studentsanswered this correctly

Important Questions on Perimeter, Area and Volume Environmental Impacts

EASY

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Practice 1>Q 3

Complete the below table. Round number to the nearest hundredth where appropriate.

Triangle's base in (cm)	Triangle's height in (cm)	Triangle's area in (square cm)
_____	$14.5$	$132$

EASY

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Practice 1>Q 3

Complete the below table. Round number to the nearest hundredth where appropriate.

Triangle's base in (cm)	Triangle's height in (cm)	Triangle's area in (square cm)
$8.4$	_____	210

EASY

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Practice 1>Q 3

Fill in a copy of this table. Round numbers to the nearest hundredth where appropriate.

Triangle's base in (cm)	Triangle's height in (cm)	Triangle's area in (square cm)
_____	$16.5$	$84$

EASY

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Practice 1>Q 3

Fill in a copy of this table. Round numbers to the nearest hundredth where appropriate.

Triangle's base in (cm)	Triangle's height in (cm)	Triangle's area in (square cm)
$10.5$	_____	$48$

EASY

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Reflect and discuss 3>Q •

What is the relationship between the area of rectangle and measurements of its side?

EASY

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Reflect and discuss 3>Q •

What is the relationship between the area of right -angled triangle and the measuremens of its sides?

MEDIUM

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Perimeter and area of a rectangle>Q 1

Perimeter (km)	Length of rectangle (km)	Width of rectangle (km)	Area of protected region ( $k m^{2}$ )
$20$	$1$
$20$	$2$
$20$
$20$
$20$	$5$
$20$
$20$
$20$	$9.8$

Calculate the area with other values of the perimeter. Which shape seems to maximize the area of the protected region?

MEDIUM

MYP:1

IMPORTANT

MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Perimeter and area of a rectangle>Q 3

Perimeter (km)	Length of rectangle (km)	Width of rectangle (km)	Area of protected region ( $k m^{2}$ )
$20$	$1$
$20$	$2$
$20$
$20$
$20$	$5$
$20$
$20$
$20$	$9.8$

Write down a generalization about the relationship between the area of a rectangle and its perimeter , when the perimeter remains constant.

Complete the below table. Round number to the nearest hundredth where appropriate. Triangle's base in (cm) Triangle's height in (cm) Triangle's area in (square cm) 10 12.6

Important Questions on Perimeter, Area and Volume Environmental Impacts

Learn and Prepare for any exam you want !

Complete the below table. Round number to the nearest hundredth where appropriate.

Triangle's base in (cm) Triangle's height in (cm) Triangle's area in (square cm)

$10$ $12.6$