Question

The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is (in sq cm)
124
118
128
112

Answer 1

Answer:

Using Pythagoras' theorem, substitute in the values of the non-parallel side and the altitude:  

10² = 8² - x²  

x² = 36  

x = 6  

Therefore the base of the right-angled triangles is 6cm.  

If we let the shorter parallel side of the trapezium = x, the longer parallel side will = x + 12.  

P = x + x + 12 + 10 + 10 = 52  

2x = 20  

x = 10  

Therefore the side lengths of the trapezium are 10, 10, 10 and 22.  

A = h/2(a + b)  

= 8/2 x 32  

= 4 x 32  

= 128cm²

Step-by-step explanation:

Answer 2

Answer :

The area of trapezium is 128 cm². [ Option c. 128cm² ]

Step-by-step explanation :

To Find,

• The area of trapezium is [ sq cm ]

Solution,

Given that,

• Perimeter of trapezium = 52cm

• The non-parallel sides of trapezium = 10cm

• Height ( distance between them ) = 8cm

To get the area of trapezium, first we need to find out the sum of parallel sides of trapezium.

A . T . Q

Let us assume the parallel sides of trapezium as x and y.

As we know that,

Perimeter of trapezium = a + b + c + d

Where,

• a, b, c and d are the sides of trapezium

∴ x + y + 10 + 10 = 52

➠ x + y + 10 + 10 = 52

➠ x + y + 20 = 52

➠ x + y = 52 - 20

➠ x + y = 32

The sum of the two parallel sides of trapezium are 32cm.

Now, we can find out the area of trapezium,

As we know that,

Area of trapezium = 1/2 × ( sum of parallel sides ) × Height

➠ 1/2 × 32 × 8 ...... dividing 8 and 2 with 2

➠ 32 × 4

➠ 128 ★

∴ The area of trapezium is 128 cm².