AP State Syllabus AP Board 7th Class Maths Solutions Chapter 13 Area and Perimeter Ex 2 Textbook Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 13th Lesson Area and Perimeter Exercise 2

Question 1.

Find the area of the each of the following parallelograms.

Solution:

Fig | Base | Height | A = Base x Height |

(i) | 7 | 4 | 7 x 4 = 28cm^{2} |

(ii) | 5 | 3 | 5 x 3 = 15 cm^{2} |

(iii) | 5.1 | 7.6 | 5.1 x 7.6 = 38.76 cm^{2} |

(iv) | 4 | 6 | 4 x 6 = 24cm^{2} |

Question 2.

PQRS is a parallelogram. PM is the height from P to \(\overline{\mathrm{SR}}\) and PN is the height from P to \(\overline{\mathrm{QR}}\). If SR = 12cm and PM = 7.6 cm.

(i) Find the area of the parallelogram PQRS

(ii) Find PN, if QR = 8 cm.

Solution:

i) Given:SR = 12cm

PM = 7.6cm

∴ Area = base × height

= 12 × 7.6 = 91.2 cm^{2}

ii) Also area = base × height

91.2 = QR × PN

91.2 = 8 × PN

∴ PN = \(\frac{91.2}{8}\) = 11.4cm

Question 3.

DF and BE are the height on sides AB and AD respectively in parallelogram ABCD. Ifthe area of the parallelogram is 1470 cm^{2}, AB = 35 cm and AD = 49 cm, find the length of BE and DF.

Solution:

Given : AB = 35 cm, AD = 49 cm

area of 🖾ABCD = 1470 cm^{2}

Area of a parallelogram = base × height

AB × DF = area of 🖾ABCD

35 × DF = 1470

DF = \(\frac{1470}{35}\) = 42cm

Also AD × BE = 1470

49 × BE = 1470

∴ BE= \(\frac{1470}{49}\) = 30cm

Question 4.

The height of a parallelogram is one third of its base. If the area of the parallelogram is 192cm^{2}, find its height and base.

Solution:

Area of the parallelogram = 192 cm^{2}

Area of parallelogram = base × height = 192 cm^{2} (given)

Let the base of the parallelogram be x.

height = \(\frac{x}{3}\)

Area = base × height = x x \(\frac{x}{3}=\frac{x^{2}}{3}\) = 192

⇒ x^{2} = 192 × 3 = 576

x = \(\sqrt{576}\) = 24

∴ base = 24 cm

height = \(\frac{x}{3}=\frac{24}{3}\) = 8cm.

Question 5.

In a parallelogram the base and height are is in the ratio of 5:2. If the area of the parallelogram is 360m^{2}, find its base and height.

Solution:

Let the base of the parallelogram be 5x and height of the parallelogram be 2x.

Area = height x base = 5x × 2x = 10x^{2} = 360 cm^{2} (given)

10x^{2} = 360

x^{2} = \(\frac{360}{10}\) = 36

x = √36 = 6

base = 5x = 5(6) = 30 cm

height = 2x = 2(6) = 12 cm

Question 6.

A square and a parallelogram have the same area. If a side of the square is 40m and the height of the parallelogram is 20m, find the base of the parallelogram.

Solution:

Given: Side of a square = 40m

Height of a parallelogram = 20m

Area of parallelogram = Area of the square

base × height side × side

base × 20 40 × 40

∴ base = \(\frac{40 \times 40}{20}\) = 80 m.