# How much paper of each shade is needed to make a kite given in Fig. 12.4, in which ABCD is a square with diagonal 44 cm.

**Solution:**

Given, ABCD is a square with diagonal 44 cm

We have to find the quantity of paper of each shade needed to make a kite as shown in

the given figure.

We know that all the sides of a square are equal.

AB = BC = CD = AD

In triangle ACD,

Given, AC = 44 cm

By using Pythagorean theorem,

AC² = AD² + DC²

Since AD = DC

(44)² = AD² + AD²

2AD² = 1936

AD² = 1936/2

AD² = 968

Taking square root,

AD = √22 × 44

= √2 × 11 × 4 × 11

= (2 × 11)√2

AD = 22√2 cm

Area of square = side × side

Area of square ABCD = AB × CD

= 22√2 × 22√2

= 968 cm²

From the figure,

We observe that the square is divided into four equal parts.

2 yellow parts, 1 green part and 1 red part.

Area of green region = 968/4 = 242 cm²

Area of red region = 968/4 = 242 cm²

Area of 2 yellow regions = 968/2 = 484 cm²

Area of green part = area of triangle PCQ

In triangle PCQ,

PC = QC = 20 cm

PQ = 14 cm

This implies PCQ is an isosceles triangle

Area of isosceles triangle = a/4 √4b² - a²

Here, a = 14 cm and b = 20 cm

= 14/4 √4(20)² - (14)²

= 7/2 √4(400) - 196

= 7/2 √1600 - 196

= 7/2 √1404

= 7/2 (37.46)

= 131.04 cm²

Area of green part = 131.04 cm²

Therefore, area of green part = 242 + 131.04

= 373.04 cm²

Therefore, the paper required for each shade to make the kite is

Yellow shade = 484 cm²

Red shade = 242 cm²

Green shade = 373.04 cm²

**✦ Try This:** Two parallel sides of a trapezium are 60 cm and 77 cm and the other sides are 25 cm and 26 cm. Find the area of the trapezium.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 12

**NCERT Exemplar Class 9 Maths Exercise 12.4 Problem 1**

## How much paper of each shade is needed to make a kite given in Fig. 12.4, in which ABCD is a square with diagonal 44 cm.

**Summary:**

The quantity of paper of each shade is needed to make a kite given in Fig. 12.4, in which ABCD is a square with diagonal 44 cm is Yellow shade = 484 cm², Red shade = 242 cm², Green shade = 373.04 cm²

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