Question

In the figure, □STNE is a rectangle. Q is the midpoint of ST then find area of the □STNE, area of ΔNTQ & area of shaded portion.​

Answer 1

Given:

□STNE is a rectangle. Q is the midpoint of ST

To find:

The area of the □STNE, area of ΔNTQ & area of the shaded portion.​

Solution:

Finding the area of the □STNE:

The area of the □STNE is,

= Area of a rectangle

= length × breadth

= SE × NE

= 12 × 18

= 216 cm²

Finding the area of Δ NTQ:

The area of the Δ NTQ is,

= Area of a triangle

= $\frac{1}{2} \times base \times height$

= $\frac{1}{2} \times QT \times NT$

∵  $QT = \frac{1}{2} ST = \frac{1}{2}NE = \frac{1}{2} \times 18 = 9\: cm\:and\:NT = SE = 12 cm$

= $\frac{1}{2} \times 9 \times 12$

= 54 cm²

Finding the area of the shaded region:

As Q is the midpoint of ST ∴ SQ = QT = 9 cm

∴ Area of ΔNTQ = Area of Δ ESQ = 54 cm²

Now,

The area of the shaded region is,

= [Area of □STNE] - [Area of ΔNTQ] - [Area of ESQ]

= 216 cm² - 54 cm² - 54 cm²

= 108 cm²

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