Gujarat Board Textbook Solutions Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

Gujarat Board Textbook Solutions Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

GSEB Solutions Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

Question 1.
A park in the shape of a quadrilateral ABCD, has ∠C = 90°,AB = 9m, BC = 12m,CD = 5m and AD = 8 m. How much area does it occupy?
Solution:
Join BD.
Area of right triangle BCD

∴ Area of the quadrilateral ΔBCD
= Area of ΔBCD + Area of ΔABD
= 30 m² + 35.5 m²
= 65.5 m² (approx.)
Hence, the park occupies the area 65.5 m² (approx.).

Question 2.
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC =5cm.
Solution:
For ΔABC
a = 4cm, b = 5cm, c = 3cm
∴ a² + c² = b²

= 2 x 4.6 cm² (approx.)
= 9.2 cm² (approx.)
∴ Area of the quadrilateral ABCD
= Area of ΔABC + Area of ΔACD
= 6 cm² + 9.2 cm²
= 15.2 cm² (approx.)

∴ Area of the quadrilateral ABCD
= Area of ÊABC + Area of ΔACD
= 6 cm² + 9.2 cm²
= 15.2 cm² (approx.)

Question 3.
Radha made a picture of an aeroplane with colored paper as shown in figure. Find the total area of the paper used.

Question 4.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Solution:
For triangle

Question 5.
A rhombus-shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
For ΔABC
a = 30m, b = 48m, c = 30m

Question 6.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

Question 7.
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and side 6 cm each is to be made of three different shades as shown in figure. How much paper of each shade has been used in it?

Question 8.
A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50 paise per cm².

Question 9.
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The nonparallel sides are 14 m and 13 m. Find the area of the field.
Solution:
Let the given field be in the shape of a trapezium ABCD in which AB = 25 m, CD = 10 m, BC = 13m and AD = 14m. FromD,drawDEIIBC meeting AB at E. Also, draw DE .L AB.

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