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Area Exercise 7.3 Class 8 Maths – Chapter 7 NCERT Solutions

NCERT Class 8 Maths Term 2 Chapter 7 Area Exercise 7.3 detailed solutions are given below. Prepared by the experts at ALLEN, these solutions are provided for easy and effective learning and to support students in their academic journey and final exam preparation.Exercise 7.3 Areas of quadrilaterals, shaded regions, regular hexagons and area fractions. It also includes a midpoint construction to obtain a quadrilateral with half the area of the given quadrilateral.

1.0Download Class 8 Maths Chapter 7 Ex 7.3 NCERT Solutions PDF

You can download the detailed Exercise 7.3 solutions provided below for practice and revision.

Chapter 7 : Area Exercise 7.3

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2.0Detailed NCERT Solutions for Area Exercise 7.3 Class 8 Maths (Ganita Prakash Term 2)

1. Find the area of the quadrilateral ABCD given that $AC = 22 cm, BM = 3 cm, DN = 3 cm, BM$ is perpendicular to AC and DN is perpendicular to AC .

Sol. Area of the quadrilateral $ABCD =$ Area of triangle $CAD +$ Area of triangle ACB Area of $△ ACB = \frac{1}{2} \times AC \times BM$ $= \frac{1}{2} \times 22 cm \times 3 cm$ $= 33 cm^{2}$ Area of $△ CAD = \frac{1}{2} \times AC \times DN$ $= \frac{1}{2} \times 22 cm \times 3 cm$ $= 33 cm^{2}$ ∴ The area of the quadrilateral $ABCD = 33 cm^{2} + 33 cm^{2} = 66 cm^{2}$

2. Find the area of the shaded region given that ABCD is a rectangle.

Sol. The area of the shaded region $=$ Area of the rectangle $ABCD -$ (Area of triangle $AEF +$ Area of triangle EBC ) Area of the rectangle ABCD $=$ Length × Breadth $= AB \times AD$ $= 18 cm \times 10 cm$ $[∵ AB = AE + EB = 10 cm + 8 cm = 18 cm;$ $AD = AF + FD = 6 cm + 4 cm = 10 cm$ ] $= 180 cm^{2}$ Area of the triangle AEF $= \frac{1}{2} \times AE \times AF$ $= \frac{1}{2} \times 10 cm \times 6 cm = 30 cm^{2}$ Area of the triangle $EBC = \frac{1}{2} \times EB \times BC$ $= \frac{1}{2} \times 8 cm \times 10 cm = 40 cm^{2}$ $∴$ The area of the shaded region $= 180$ $cm^{2} - (30 cm^{2} + 40 cm^{2})$ $= 180 cm^{2} - 70 cm^{2}$ $= 110 cm^{2}$ 3. What measurements would you need to find the area of a regular hexagon?

Sol. Side length ( $ℓ$ ) of the hexagon needed to find the area of regular hexagon.

4. What fraction of the total area of the rectangle is the area of the blue region?

Sol. Let $ℓ$ be the length and b be the breadth of the rectangle ABCD .

Total area of rectangle, $ABCD = DC \times BC = ℓ \times$ b sq. units

Area of $△ AOB = \frac{1}{2} \times AB \times OE = \frac{1}{2} \times ℓ \times xsq$ . units Area of $△ DOC = \frac{1}{2} \times DC \times OF = \frac{1}{2} \times ℓ \times y$ sq. units ∴ The area of the blue region

$= Area of △ AOB + Area of △ DOC = \frac{1}{2} \times ℓ \times x + \frac{1}{2} \times ℓ \times y = \frac{1}{2} \times ℓ \times (x + y) sq. units$ $= \frac{1}{2} \times ℓ \times b sq. units [∴ x + y = b]$

∴ Area of blue region $= \frac{1}{2} \times$ Area of rectangle Thus, the required fraction is $\frac{1}{2}$ .

5. Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral. Sol. Let ABCD be a given quadrilateral.

Mark mid points of $AB, BC, CD$ and DA as P, Q, R and S. Join midpoints, then PQRS is the required quadrilateral with half the area of the given quadrilateral ABCD .

3.0Key Concepts of Chapter 7 Area Exercise 7.3

Finding the area of a quadrilateral by dividing it into two triangles.
Using a diagonal and perpendicular distances to calculate the area of a quadrilateral.
Determining the area of a shaded region by subtracting triangular areas from a rectangle.
Identifying the measurement required to calculate the area of a regular hexagon.
Expressing the area of a region as a fraction of the total rectangle area.
Constructing a quadrilateral with half the area of a given quadrilateral using the midpoints of its sides.

4.0Benefits of NCERT Solutions Class 8 Maths Chapter 7 Exercise 7.3

Divides a quadrilateral into triangles to work out its area.
Uses perpendicular distances from a diagonal to determine the areas of triangles.
Calculates shaded areas by subtracting the areas of unshaded triangles from a rectangle.
Identifies the measurement required to find the area of a regular hexagon.
Represents the area of a region as a fraction of the total rectangle area.
Uses the midpoints of the sides of a quadrilateral to construct a figure with half its area.

NCERT Class 8 Maths Ch. 7 Area Other Exercises:-

Exercise 7.1

Exercise 7.2