A design is made up of four congruent right triangles as shown in Fig. 9.63. Find the area of the shaded portion.
Solution:
Given, a design is made up of four congruent right triangles.
We have to find the area of the shaded region.
Consider the square ABCD,
Side of square = 30 + 10 = 40 cm
Area of square = (side)²
= (40)²
= 1600 cm²
Considering one right angled triangle BGH,
Area of triangle = 1/2 × base × height
Area of triangle BGH = 1/2 × BH × BG
= 1/2 × 10 × 30
= 10(15)
= 150 cm²
Since the triangles are congruent,
Area of 4 triangles = 4(150)
= 600 cm²
Area of the shaded portion = area of square - area of 4 congruent triangles
= 1600 - 600
= 1000 cm²
Therefore, the area of the shaded portion is 1000 cm².
✦ Try This: Find the perimeter of the given figure.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 118
A design is made up of four congruent right triangles as shown in Fig. 9.63. Find the area of the shaded portion.
Summary:
A design is made up of four congruent right triangles as shown in Fig. 9.63. The area of the shaded portion is 1000 cm².
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