Blog

Examples 1 to 5 of Mensuration

No Comments

(1) Find the area of a square, one of whose diagonals measures 50 cm.

Soln. Area of the square = $\frac{1}{2} \times$ ( Diagonal ) ² = $\frac{1}{2}\times$ ( 50 )² = 1250 cm².

(2) One side of a rectangular field is 24m and one of its diagonals is 26 m. Find the area of the field.

Soln.

Other side = $\sqrt{26^2-24^2}$ = 10 m.

$\therefore$ Area = l b

= ( 24 $\times$ 10 ) m² = 240 m².

(3) Find the area of a rhombus whose diagonals are 10 cm and 12 cm.

Soln. Area of rhombus = $\frac{1}{2} \times 10 \times 12$ = 60 sq. cm.

(4) Find the area of a rhombus each one of whose sides measures 20 cm and one diagonal 24 cm.

Soln. Here, AB = BC = CD = DA = 20 m &

Let, AC = 24 m $\therefore$ AM = 12 m

Now, in right angled $\mathrm{\Delta}$ AMB, by Pythagoras’ law,

AM² + BM² = AB²

∴ BM = 16 BD = 32 m

Now,

Area of rhombus = × ( AC × BD ) = × ( 24 × 32 ) cm² = 384 cm².

(5) Find the area of a right angled triangle whose base is 3 m and hypotenuse 5 m.

Soln. Height = $\sqrt{5^2-3^2}$ = 4 m.

∴ Area = $\frac{1}{2}$ × Base × Height = $\frac{1}{2}$ × 3 × 4 = 6 m².