Question

20. The base of an isosceles triangle is 16 cm. If
the height on the base is 4 cm shorter than the
equal sides, find the area of the triangle.
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

The area of triangle is 48 cm².

Given - Base and height

Find - Area of triangle

Solution - Let the each equal sides of triangle be x cm. So, height of triangle = (x - 4) cm

Now, using Pythagoras theorem to find the value of x.

The half right angled triangle will be used for calculation, hence, base will be = $\frac{16}{2}$

Base = 8 cm

Hypotenuse² = Base² + Perpendicular²

x² = 8² + (x - 4)²

Expanding the perpendicular expression

x² = 8² + x² + 16 + 8x

x² is common on both sides and hence will be cancelled

Rewriting the equation -

8x = 64 + 16

8x = 80

$x = \frac{80}{8}$

Performing Division

x = 10 cm

So, height = x - 4

Height = 10 - 4

Height = 6 cm

Now, calculating area of isosceles triangle by the formula -

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

Area = $\frac{1}{2} \times 16 \times 6$

Area = $8 \times 6$

Area = 48 cm²

Hence, the area of triangle is 48 cm².

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